math presentation
Download as PPT, PDF0 likes75 views
This document provides definitions and examples related to different types of angles in geometry. It defines a line segment, straight line, and ray. It then discusses the measurement of angles using a protractor and defines different types of angles including acute, right, obtuse, straight, and reflex angles. Examples are given of classifying angles based on their degree measures. Students are assigned an exercise to define the type of each angle in a diagram and homework from the workbook.
1 of 26
Download to read offline
Recommended
3-1 Classifying and Labeling Angles
3-1 Classifying and Labeling Anglesgwilson8786
油
This document defines and describes angles. It discusses the different types of angles including acute, right, obtuse, and straight angles. It explains how to measure angles using a protractor and name angles using symbols. Examples are provided to demonstrate how to measure angles on a protractor and draw an angle that measures a specific degree, such as 60 degrees.5 1 classifying triangles
5 1 classifying trianglesgwilson8786
油
There are 7 types of triangles classified by their sides and angles: equilateral triangles have 3 congruent sides; isosceles triangles have 2 congruent sides; scalene triangles have no congruent sides; equiangular triangles have 3 congruent angles; acute triangles have 3 acute angles; obtuse triangles have 1 obtuse angle; and right triangles have 1 right angle. The lesson teaches how to classify triangles based on these properties of their sides and angles.Sum Of The Angles Of A Triangle
Sum Of The Angles Of A Trianglecorinnegallagher
油
This document discusses the angles of triangles. It explains that the three angles of any triangle will sum to 180 degrees. If two angles of a triangle are known, the third unknown angle can be found by subtracting the two known angles from 180 degrees. Examples are provided to demonstrate finding the measure of the unknown third angle of a triangle given two other angle measures.Angles and their measures
Angles and their measuresQalbay Abbas
油
This document defines angles and their measures. It discusses that an angle consists of two rays with a common vertex point. The measure of an angle is denoted by m and can be approximated using a protractor in degrees. Angles with the same measure are congruent. The document also covers classifying angles as acute, right, obtuse, or straight based on their measure. Additionally, it discusses adjacent angles and the angle addition postulate.geometry m1
geometry m1mehreenfathima2
油
This document covers different topics in geometry including points, lines, line segments, rays, angles, and measuring angles. It defines each term and provides examples. Points have position but no size, a line extends indefinitely, a line segment connects two points, a ray has an endpoint and extends in one direction, and an angle is formed by two rays with a common endpoint. The document explains how to measure angles using a protractor and the degree unit, and provides practice examples of finding the measure of different angles.Math12 lesson9
Math12 lesson9KathManarang
油
The document derives the Law of Sines and Law of Cosines, which relate the angles and sides of triangles. It discusses using these laws to solve oblique triangles given certain information like two angles and a side, two sides and the angle opposite one of the sides, two sides and the angle between them, or all three sides. It also covers finding the area of a triangle given two sides and the included angle, or using Heron's Formula with all three sides. Application problems demonstrate using these concepts to solve real-world geometry problems.Constructing triangles
Constructing trianglesCnavarrovargas
油
1. The document provides instructions for constructing different types of triangles given specific properties: equilateral triangles given one side, isosceles triangles given two sides, scalene triangles given three sides, and right triangles given the hypotenuse and one leg.
2. The steps involve using a compass to draw arcs with the given side lengths and finding the point of intersection to determine the third vertex.
3. Lines are then drawn between the vertices to complete the triangle.17 2
17 2Dan O'Brien
油
Two rays with a common endpoint form an angle, with the vertex being their point of intersection. Angles are measured in degrees using a protractor, from 0 to 180 degrees. There are four main types of angles: right angles measuring 90 degrees and forming a square; acute angles between 0 and 90 degrees; obtuse angles between 90 and 180 degrees; and straight angles measuring 180 degrees and forming a straight line.Oblique triangles
Oblique triangleslhance Leopar
油
The document discusses trigonometric methods for solving oblique triangles. It defines sine law as relating each side of a triangle to the sine of its opposite angle. Sine law is used when the given data includes a side and its opposite angle. Cosine law defines the square of any side as the sum of the squares of the other two sides minus twice the product of those sides times the cosine of the angle between them. Cosine law can be used to solve for any side or angle of a triangle given the other two sides and their included angle.Perpendicular lines
Perpendicular linesCnavarrovargas
油
The document describes how to construct perpendicular lines in four situations:
1) Drawing the line bisector of a line segment which is perpendicular to the segment and passes through its midpoint.
2) Drawing a perpendicular line to a given ray from its endpoint by centering compass arcs on the endpoint.
3) Drawing a perpendicular line to a given line from a point on the line by centering arcs on the point and finding bisectors.
4) Drawing a perpendicular line to a given line from an external point by centering arcs on the point and finding bisectors.Oblique triangles made by: MR. ROLAND M. LEOPAR
Oblique triangles made by: MR. ROLAND M. LEOPARlhance Leopar
油
This document discusses oblique triangles and the sine law and cosine law for solving triangles. It provides examples of applying these laws to find missing angles and sides of triangles given various parts of triangles, such as two sides and the included angle, two angles and the included side, or three sides. The seven examples show step-by-step workings of applying the sine and cosine laws to find the missing parts in different triangle scenarios.Angles
AnglesPunita Verma
油
Angles are measured in degrees. An acute angle measures between 0 and 90 degrees, an obtuse angle measures between 90 and 180 degrees, and a right angle measures exactly 90 degrees. Two angles are complementary if their measures sum to 90 degrees, and two angles are supplementary if their measures sum to 180 degrees. Vertical angles are angles opposite each other when two lines intersect, and vertical angles have the same degree measurement.Law Of Sines; Powerpoint
Law Of Sines; Powerpointguesta69721
油
The document discusses the Law of Sines, which can be used to solve triangles that are not right triangles. It provides three formulas for finding the area of a triangle using two angles and one included side: Area = 1/2 * b * c * sin(A), 1/2 * a * c * sin(B), 1/2 * a * b * sin(C). It also gives the formula for the Law of Sines: a/sin(A) = b/sin(B) = c/sin(C). An example problem finds the area of a triangle given two side lengths and one angle measure.Trigonometry
TrigonometrySanpraju
油
This PowerPoint presentation covers trigonometry and solving triangles using trigonometric functions and identities. It introduces trigonometric ratios like sine, cosine, and tangent and how they are used to solve right triangles. It then covers solving both right and oblique triangles using the Law of Sines and Law of Cosines. The presentation also discusses trigonometric identities and conversions between degrees and radians. Examples are provided to demonstrate solving triangles using the concepts introduced.Basic operations review
Basic operations reviewCnavarrovargas
油
The document provides step-by-step instructions for performing basic geometry operations using a compass and straightedge. It includes exercises for drawing perpendicular bisectors, dividing a line segment into equal parts, constructing angle bisectors, and performing angle additions and subtractions by copying angles onto a reference arc. The instructions are broken down into clear individual steps with diagrams to illustrate each step.Perpendicular bisector
Perpendicular bisectorCnavarrovargas
油
The document describes the steps to draw a perpendicular bisector of a line segment. The steps are:
1) Center a compass at one end of the segment and draw an arc past the middle of the segment.
2) Repeat at the other end of the segment.
3) The point where the arcs intersect is where the perpendicular bisector is drawn between.The Law of Cosines demo
The Law of Cosines demoReymark Velasco
油
This document discusses the law of sines and law of cosines for solving oblique triangles. It provides examples of using each formula to find missing sides or angles. The law of sines is used when two angles and a non-included side or two sides and the angle opposite one side are given. The law of cosines is used when two sides and the included angle or all three sides are given. An example problem demonstrates applying the law of cosines to find the missing side of a triangle given two sides and one angle. Students will complete an in-class activity and homework applying these formulas to additional triangles.8 teorema phytagoras 2
8 teorema phytagoras 2Eva Nurmalasari
油
The document discusses the Pythagorean theorem and properties of triangles. It contains an example problem calculating the length of one side of a right triangle given the lengths of the other two sides using the Pythagorean theorem. It then lists and defines the different types of lines that can be drawn in a triangle, including altitudes, medians, angle bisectors, and perpendicular bisectors.construction (maths)
construction (maths)Pratap Kumar
油
The document describes several methods for constructing angles and triangles using only a compass and straightedge. It provides step-by-step instructions on how to construct: an angle bisector; common angles like 60 and 90 degrees; equilateral and isosceles triangles given various parameters; and a triangle given its perimeter and two base angles. Justifications are given explaining how each construction method divides angles or lengths as needed to satisfy the required properties.4th l6. oblique triangle
4th l6. oblique trianglerina valencia
油
Here are the steps to solve this problem:
a. AC is the hypotenuse of the right triangle ABC.
We are given that AB = 6 units
and angle BAC = 45 degrees
Using the trigonometric identity that sin(45) = 0.5, we can set up:
sin(45) = opposite/hypotenuse
0.5 = AB/AC
AC = AB/sin(45)
AC = 6/0.5 = 12 units
b. To find BC, we can use the Pythagorean theorem since this is a right triangle:
BC^2 = AB^2 + AC^2 - 2AB*ACcos(B)
BCAngles and properties for class VII by G R Ahmed
Angles and properties for class VII by G R AhmedMD. G R Ahmed
油
The document defines different types of angles and their properties. It explains what an angle is, how angles are named and measured. It discusses right angles, straight angles, acute angles, obtuse angles and reflex angles. It describes angles on a straight line, angles at a point, intersecting lines, parallel lines, perpendicular lines, vertically opposite angles, corresponding angles and alternate angles. It presents proofs of several theorems regarding the sum of interior and exterior angles of triangles.Drawing with the bisector of an angle
Drawing with the bisector of an angleCnavarrovargas
油
The document provides steps for drawing a fan by bisecting angles. It involves initially dividing a 90 degree angle in half, then bisecting those 45 degree angles to create four equal angles. Arcs are drawn using a compass to locate bisectors and intersection points, dividing the angles further. Finally, a semicircle is drawn to complete the fan shape, using the original diameter as the radius.Operations with angles
Operations with anglesCnavarrovargas
油
The document provides step-by-step instructions for performing operations on angles using a compass, including copying an angle, drawing an angle bisector, adding angles, subtracting angles, and performing multiple operations on angles. Specific steps include drawing arcs using a compass, measuring distances between points on arcs, and transporting those distances to draw angles on different rays. An example is worked through applying these steps to add, subtract and combine adding and subtracting for given angles A, B and C.
Introduction to Trigonometry
Introduction to Trigonometrynayyab imdad
油
This document introduces trigonometry, including:
- Trigonometry is the measurement of triangles and the relationship between sides and angles, derived from Greek words meaning "three", "angles", and "measurement".
- Angles are formed by two rays with a common starting point and can be positive or negative depending on direction of rotation.
- Trigonometric functions relate ratios of sides of a right triangle to an angle and include sine, cosine, tangent, cotangent, secant, and cosecant.
- Fundamental trigonometric identities are derived, including that sine squared plus cosine squared equals one.Drawing perpendicular lines
Drawing perpendicular linesCnavarrovargas
油
The document provides steps for drawing perpendicular and parallel lines using a compass. It describes how to draw:
1) The perpendicular to a line through an external point.
2) The perpendicular to a line through a point on the line.
3) The perpendicular to a ray at its endpoint.
4) A parallel line to a given line passing through an external point.
The steps involve drawing arcs intersecting the lines from various points to locate points, then joining points to draw the perpendicular or parallel lines.Drawing circumferences
Drawing circumferencesCnavarrovargas
油
The document describes four exercises for drawing circumferences based on given geometric properties: 1) Drawing a circumference from two endpoints of a diameter. 2) Finding the center of a circumference from three points on an arc. 3) Drawing a circumference through three given points. 4) Drawing a circumference tangent to a given line, with the center and tangency point also given. The steps provided for each exercise involve drawing perpendicular bisectors and determining the intersection point that identifies the center.Angle for class VI & VII
Angle for class VI & VIIMD. G R Ahmed
油
The document defines different types of angles and their properties. It explains that an angle is formed when two lines meet at a vertex point. Angles can be measured and classified as acute, obtuse, right or reflex depending on their degree measure. The relationships between angles formed by parallel and intersecting lines are also described, including that vertically opposite, corresponding, and alternate angles are equal. Pairs of lines can be intersecting, parallel, or perpendicular.Introduction to trigonometry 
Introduction to trigonometry Gayathri Gaya
油
This document discusses trigonometric ratios and identities. It defines trigonometric ratios as relationships between sides and angles of a right triangle. Specific ratios are defined for angles of 0, 30, 45, 60, and 90 degrees. Complementary angle identities are examined, showing ratios are equal for complementary angles (e.g. sin(90-A)=cos(A)). Trigonometric identities are derived from the Pythagorean theorem, including cos^2(A) + sin^2(A) = 1, sec^2(A) = 1 + tan^2(A), and cot^2(A) + 1 = cosec^2(A). Examples are provided to demonstrate using identities whenIntroduction To Trigonometry
Introduction To TrigonometryAbhay and Parth
油
This document provides an introduction to trigonometric ratios and identities. It defines the six trigonometric ratios (sine, cosine, tangent, cotangent, secant, cosecant) for an acute angle in a right triangle. It gives the specific trigonometric ratios for angles of 0属, 45属, 30属, 60属, and 90属. It also establishes the identities relating trigonometric ratios of complementary angles and the Pythagorean identities relating sine, cosine, tangent, cotangent, secant, and cosecant. Examples are provided to demonstrate how to use trigonometric identities to determine ratios when one ratio is known.More Related Content
What's hot (20)
Oblique triangles
Oblique triangleslhance Leopar
油
The document discusses trigonometric methods for solving oblique triangles. It defines sine law as relating each side of a triangle to the sine of its opposite angle. Sine law is used when the given data includes a side and its opposite angle. Cosine law defines the square of any side as the sum of the squares of the other two sides minus twice the product of those sides times the cosine of the angle between them. Cosine law can be used to solve for any side or angle of a triangle given the other two sides and their included angle.Perpendicular lines
Perpendicular linesCnavarrovargas
油
The document describes how to construct perpendicular lines in four situations:
1) Drawing the line bisector of a line segment which is perpendicular to the segment and passes through its midpoint.
2) Drawing a perpendicular line to a given ray from its endpoint by centering compass arcs on the endpoint.
3) Drawing a perpendicular line to a given line from a point on the line by centering arcs on the point and finding bisectors.
4) Drawing a perpendicular line to a given line from an external point by centering arcs on the point and finding bisectors.Oblique triangles made by: MR. ROLAND M. LEOPAR
Oblique triangles made by: MR. ROLAND M. LEOPARlhance Leopar
油
This document discusses oblique triangles and the sine law and cosine law for solving triangles. It provides examples of applying these laws to find missing angles and sides of triangles given various parts of triangles, such as two sides and the included angle, two angles and the included side, or three sides. The seven examples show step-by-step workings of applying the sine and cosine laws to find the missing parts in different triangle scenarios.Angles
AnglesPunita Verma
油
Angles are measured in degrees. An acute angle measures between 0 and 90 degrees, an obtuse angle measures between 90 and 180 degrees, and a right angle measures exactly 90 degrees. Two angles are complementary if their measures sum to 90 degrees, and two angles are supplementary if their measures sum to 180 degrees. Vertical angles are angles opposite each other when two lines intersect, and vertical angles have the same degree measurement.Law Of Sines; Powerpoint
Law Of Sines; Powerpointguesta69721
油
The document discusses the Law of Sines, which can be used to solve triangles that are not right triangles. It provides three formulas for finding the area of a triangle using two angles and one included side: Area = 1/2 * b * c * sin(A), 1/2 * a * c * sin(B), 1/2 * a * b * sin(C). It also gives the formula for the Law of Sines: a/sin(A) = b/sin(B) = c/sin(C). An example problem finds the area of a triangle given two side lengths and one angle measure.Trigonometry
TrigonometrySanpraju
油
This PowerPoint presentation covers trigonometry and solving triangles using trigonometric functions and identities. It introduces trigonometric ratios like sine, cosine, and tangent and how they are used to solve right triangles. It then covers solving both right and oblique triangles using the Law of Sines and Law of Cosines. The presentation also discusses trigonometric identities and conversions between degrees and radians. Examples are provided to demonstrate solving triangles using the concepts introduced.Basic operations review
Basic operations reviewCnavarrovargas
油
The document provides step-by-step instructions for performing basic geometry operations using a compass and straightedge. It includes exercises for drawing perpendicular bisectors, dividing a line segment into equal parts, constructing angle bisectors, and performing angle additions and subtractions by copying angles onto a reference arc. The instructions are broken down into clear individual steps with diagrams to illustrate each step.Perpendicular bisector
Perpendicular bisectorCnavarrovargas
油
The document describes the steps to draw a perpendicular bisector of a line segment. The steps are:
1) Center a compass at one end of the segment and draw an arc past the middle of the segment.
2) Repeat at the other end of the segment.
3) The point where the arcs intersect is where the perpendicular bisector is drawn between.The Law of Cosines demo
The Law of Cosines demoReymark Velasco
油
This document discusses the law of sines and law of cosines for solving oblique triangles. It provides examples of using each formula to find missing sides or angles. The law of sines is used when two angles and a non-included side or two sides and the angle opposite one side are given. The law of cosines is used when two sides and the included angle or all three sides are given. An example problem demonstrates applying the law of cosines to find the missing side of a triangle given two sides and one angle. Students will complete an in-class activity and homework applying these formulas to additional triangles.8 teorema phytagoras 2
8 teorema phytagoras 2Eva Nurmalasari
油
The document discusses the Pythagorean theorem and properties of triangles. It contains an example problem calculating the length of one side of a right triangle given the lengths of the other two sides using the Pythagorean theorem. It then lists and defines the different types of lines that can be drawn in a triangle, including altitudes, medians, angle bisectors, and perpendicular bisectors.construction (maths)
construction (maths)Pratap Kumar
油
The document describes several methods for constructing angles and triangles using only a compass and straightedge. It provides step-by-step instructions on how to construct: an angle bisector; common angles like 60 and 90 degrees; equilateral and isosceles triangles given various parameters; and a triangle given its perimeter and two base angles. Justifications are given explaining how each construction method divides angles or lengths as needed to satisfy the required properties.4th l6. oblique triangle
4th l6. oblique trianglerina valencia
油
Here are the steps to solve this problem:
a. AC is the hypotenuse of the right triangle ABC.
We are given that AB = 6 units
and angle BAC = 45 degrees
Using the trigonometric identity that sin(45) = 0.5, we can set up:
sin(45) = opposite/hypotenuse
0.5 = AB/AC
AC = AB/sin(45)
AC = 6/0.5 = 12 units
b. To find BC, we can use the Pythagorean theorem since this is a right triangle:
BC^2 = AB^2 + AC^2 - 2AB*ACcos(B)
BCAngles and properties for class VII by G R Ahmed
Angles and properties for class VII by G R AhmedMD. G R Ahmed
油
The document defines different types of angles and their properties. It explains what an angle is, how angles are named and measured. It discusses right angles, straight angles, acute angles, obtuse angles and reflex angles. It describes angles on a straight line, angles at a point, intersecting lines, parallel lines, perpendicular lines, vertically opposite angles, corresponding angles and alternate angles. It presents proofs of several theorems regarding the sum of interior and exterior angles of triangles.Drawing with the bisector of an angle
Drawing with the bisector of an angleCnavarrovargas
油
The document provides steps for drawing a fan by bisecting angles. It involves initially dividing a 90 degree angle in half, then bisecting those 45 degree angles to create four equal angles. Arcs are drawn using a compass to locate bisectors and intersection points, dividing the angles further. Finally, a semicircle is drawn to complete the fan shape, using the original diameter as the radius.Operations with angles
Operations with anglesCnavarrovargas
油
The document provides step-by-step instructions for performing operations on angles using a compass, including copying an angle, drawing an angle bisector, adding angles, subtracting angles, and performing multiple operations on angles. Specific steps include drawing arcs using a compass, measuring distances between points on arcs, and transporting those distances to draw angles on different rays. An example is worked through applying these steps to add, subtract and combine adding and subtracting for given angles A, B and C.Introduction to Trigonometry
Introduction to Trigonometrynayyab imdad
油
This document introduces trigonometry, including:
- Trigonometry is the measurement of triangles and the relationship between sides and angles, derived from Greek words meaning "three", "angles", and "measurement".
- Angles are formed by two rays with a common starting point and can be positive or negative depending on direction of rotation.
- Trigonometric functions relate ratios of sides of a right triangle to an angle and include sine, cosine, tangent, cotangent, secant, and cosecant.
- Fundamental trigonometric identities are derived, including that sine squared plus cosine squared equals one.Drawing perpendicular lines
Drawing perpendicular linesCnavarrovargas
油
The document provides steps for drawing perpendicular and parallel lines using a compass. It describes how to draw:
1) The perpendicular to a line through an external point.
2) The perpendicular to a line through a point on the line.
3) The perpendicular to a ray at its endpoint.
4) A parallel line to a given line passing through an external point.
The steps involve drawing arcs intersecting the lines from various points to locate points, then joining points to draw the perpendicular or parallel lines.Drawing circumferences
Drawing circumferencesCnavarrovargas
油
The document describes four exercises for drawing circumferences based on given geometric properties: 1) Drawing a circumference from two endpoints of a diameter. 2) Finding the center of a circumference from three points on an arc. 3) Drawing a circumference through three given points. 4) Drawing a circumference tangent to a given line, with the center and tangency point also given. The steps provided for each exercise involve drawing perpendicular bisectors and determining the intersection point that identifies the center.Angle for class VI & VII
Angle for class VI & VIIMD. G R Ahmed
油
The document defines different types of angles and their properties. It explains that an angle is formed when two lines meet at a vertex point. Angles can be measured and classified as acute, obtuse, right or reflex depending on their degree measure. The relationships between angles formed by parallel and intersecting lines are also described, including that vertically opposite, corresponding, and alternate angles are equal. Pairs of lines can be intersecting, parallel, or perpendicular.Similar to math presentation (20)
Introduction to trigonometry
Introduction to trigonometry Gayathri Gaya
油
This document discusses trigonometric ratios and identities. It defines trigonometric ratios as relationships between sides and angles of a right triangle. Specific ratios are defined for angles of 0, 30, 45, 60, and 90 degrees. Complementary angle identities are examined, showing ratios are equal for complementary angles (e.g. sin(90-A)=cos(A)). Trigonometric identities are derived from the Pythagorean theorem, including cos^2(A) + sin^2(A) = 1, sec^2(A) = 1 + tan^2(A), and cot^2(A) + 1 = cosec^2(A). Examples are provided to demonstrate using identities whenIntroduction To Trigonometry
Introduction To TrigonometryAbhay and Parth
油
This document provides an introduction to trigonometric ratios and identities. It defines the six trigonometric ratios (sine, cosine, tangent, cotangent, secant, cosecant) for an acute angle in a right triangle. It gives the specific trigonometric ratios for angles of 0属, 45属, 30属, 60属, and 90属. It also establishes the identities relating trigonometric ratios of complementary angles and the Pythagorean identities relating sine, cosine, tangent, cotangent, secant, and cosecant. Examples are provided to demonstrate how to use trigonometric identities to determine ratios when one ratio is known.Triangle
TriangleNur Endah Purnaningsih
油
This document provides information about different types of triangles categorized by side lengths, angle measures, and combinations of sides and angles. It defines equilateral, isosceles, scalene, acute, right, and obtuse triangles. It also discusses calculating the perimeter and area of triangles. The key points are:
- Triangles can be categorized based on equal or unequal side lengths or by angle measures.
- The sum of the interior angles of any triangle is always 180 degrees.
- The perimeter of a triangle is the sum of the lengths of its three sides.
- The area of a triangle can be calculated by multiplying one-half the base by the height.Triangle
TriangleNur Endah Purnaningsih
油
This document provides information about different types of triangles categorized by side lengths, angle measures, and combinations of sides and angles. It defines equilateral, isosceles, scalene, right, acute, and obtuse triangles. Examples are given to illustrate each type. Formulas for calculating the perimeter and area of triangles are presented. Exercises are included for the student to practice determining perimeters, areas, and drawing different triangle types.Line segment operations
Line segment operationsCnavarrovargas
油
The document describes various operations that can be performed on line segments, including copying a line segment, adding line segments, subtracting line segments, multiplying a line segment by a scalar, and dividing a line segment into equal parts. Specific step-by-step instructions are provided for how to construct or manipulate line segments to achieve each type of operation using a compass and straightedge.Mathematics Form 1-Chapter 8 lines and angles KBSM of form 3 chp 1 ...
Mathematics Form 1-Chapter 8 lines and angles KBSM of form 3 chp 1 ...KelvinSmart2
油
This document contains notes on lines and angles from mathematics Form 3. It reviews concepts from Form 1 such as classifying angles and defining parallel and perpendicular lines. It then introduces new concepts like transversals, corresponding angles, interior angles, and alternate angles formed when a line crosses two parallel lines. It provides examples of using angle properties to solve problems involving triangles and quadrilaterals. Finally, it includes sample exercises involving finding missing angle measures using the properties of parallel lines crossed by a transversal.CABT Math 8 - Angles and Angle Measurements
CABT Math 8 - Angles and Angle MeasurementsGilbert Joseph Abueg
油
The document provides information about angles and angle measurement:
- An angle consists of two rays with a common vertex point. Angles can be named using the vertex point and the rays.
- The measure of an angle is the amount of rotation between the rays, measured in degrees using a protractor. Examples of different angle measures are provided.
- Angles are classified as acute, right, obtuse or straight based on their degree measures. Concepts of complementary, supplementary, adjacent, vertical and linear pairs of angles are introduced along with related properties and theorems.
- Several examples problems demonstrate finding missing angle measures using properties of different angle relationships.Math 7 geometry 03 angles and angle measurements
Math 7 geometry 03 angles and angle measurementsGilbert Joseph Abueg
油
The document discusses various topics relating to angles and angle measurement:
1. It defines an angle and describes how to name angles using vertex notation.
2. It explains that the measure of an angle is the amount of rotation in degrees and introduces tools like protractors for measuring angles.
3. It classifies angles as acute, right, obtuse or straight based on their degree measures and defines complementary and supplementary angle pairs.Buksis 7.1 new
Buksis 7.1 newNur Endah Purnaningsih
油
This document provides information about angles and how to identify, measure, and classify different types of angles. It discusses key angle terms like acute, obtuse, right, and straight angles. It also explains how to use a protractor to measure angles and introduces different angle relationships formed when two lines are intersected by a transversal, such as corresponding angles, alternate interior angles, and vertical angles. Students are provided examples to estimate and measure angles, identify angle components, and investigate angle properties.Basics of-geometry-14562
Basics of-geometry-14562akcutway
油
The document introduces some basic concepts in geometry, including:
- Points, lines, and planes are the undefined terms that form the foundations of geometry.
- A point has no dimension, a line extends in one dimension, and a plane extends in two dimensions.
- Geometric figures can intersect if they share one or more points in common. The intersection of two lines is a point, two planes intersect along a line, and a line and plane intersect at a point.
- Other concepts introduced are line segments, rays, angles, and classifications of angles as acute, right, obtuse or straight.vectors
vectorsMohammed Ahmed
油
- A particle starts from the point with position vector (3i + 7j) m and then moves with constant velocity (2i j) ms-1. The question asks to find the position vector of the particle 4 seconds later.
- Substituting the values into the displacement equation gives the final position vector as (12i + 3j) m.
- A second particle is given a position vector of (2i + 4j) m at time t = 0 and a position vector of (12i + 16j) m five seconds later. Using the displacement equation gives the velocity of the particle as (2i + 4j) ms-1.
- For a third particle
Edm 1 lines and angles
Edm 1 lines and anglesMike
油
Lines and line segments can be measured and named using points labeled with letters. Lines extend indefinitely while line segments have distinct endpoints. Two line segments that intersect form angles, with the point of intersection called the vertex. Angles are named using the vertex letter in the middle. A right angle measures 90 degrees and is formed by perpendicular lines or line segments. Acute angles are less than 90 degrees while obtuse angles are greater than 90 degrees. Parallel lines never intersect even if extended indefinitely.Mathematics 7: Angles (naming, types and how to measure them)
Mathematics 7: Angles (naming, types and how to measure them)Romne Ryan Portacion
油
An angle is defined as the amount of turn between two straight lines that share a common endpoint called the vertex. Angles are measured in degrees using a protractor and can be acute (between 0-90 degrees), right (90 degrees), obtuse (between 90-180 degrees), or straight (180 degrees). Angles can be named using the vertex letter and the first letters of the lines that form the angle, such as BAC.Lines
LinesEdna Villanueva
油
The document explains how to factor two special types of quadratic expressions: perfect square trinomials which can be factored into two identical binomials of the form (ax+b)(ax+b), and the difference of perfect squares which can be factored as (a-b)(a+b). It provides examples of perfect square trinomials and the difference of perfect squares in factored and unfactored form, and includes practice problems for factoring these special products.vectors
vectorsMohammed Ahmed
油
This document introduces vectors and how they can be used to describe displacements and solve problems involving displacement. It discusses that vectors have both direction and magnitude, and provides examples. Vectors can be added and represented using line segments. The triangle law of addition allows vectors to be added using a triangle. Vectors can also be described using i and j notation, where i and j are unit vectors along the x and y axes, and any two-dimensional vector can be written as ai + bj. Problems can then be solved by adding or subtracting the i and j terms. The magnitude of a vector can be found using Pythagoras' theorem, and the angle between a vector and an axis can be found using trigCircles vocab and properties
Circles vocab and propertiesOlaug S
油
Circle Geometry is rich with new vocabulary (words, etcetera), especially at standard 9 (Grade 11).
Vocab is very very important in geometry. Learners' need to understand the terms/ words and the educators' must enforce the use of these terms. Circles vocab and properties
Circles vocab and propertiesThabang Nombewu
油
This document defines key terms and properties related to circles. It discusses concepts like radius, diameter, chord, tangent, arc, angle, and properties such as parallel lines intercepting congruent arcs and the measure of a central angle being twice an inscribed angle intercepting the same arc. Formulas for circumference using radius or diameter and for area in terms of radius are also provided.Circles vocab and properties
Circles vocab and propertiesThabang Nombewu
油
The most vivid concept in High school Math! Working towards build positive stigma to learners on Geometry concept.Angles
AnglesPunita Verma
油
This presentation defines and explains different types of angles. It begins by defining an angle as being formed by two rays with a common endpoint, called the vertex. It then discusses naming angles, types of angles such as acute, obtuse, right, zero and reflex angles. It also covers pairs of angles including complementary angles which sum to 90 degrees, supplementary angles which sum to 180 degrees, adjacent angles which share a vertex and side but not an interior section, vertically opposite angles formed by two intersecting lines, and linear pairs which are adjacent angles that sum to 180 degrees.math presentation
- 2. Our lesson today in.. Geometry
- 3. Firstly. Whats the deference between,
- 4. ExcellentExcellent,, As you noticedAs you noticed!!!!
- 5. We called them.. Line segment, Straight line And Ray
- 6. DefinitionsDefinitions:: A line segment: A set of points..consisting of 2 distinct points like A and B (when we join them by a ruler( AB俗=BA俗 We can`t draw more than 1 line segment joining 2 points It has 2 ends points It has length A B
- 7. DefinitionsDefinitions:: A straight line: Has an infinite number of points on it. The 2 arrows show that it can be extended without limit on its 2 sides AB俗=BA俗 We can`t draw more than 1 straight line joining 2 points. It has no starting point and no ending point sowe cant measure its length. A B
- 8. DefinitionsDefinitions:: A Ray: The line segment AB俗 and all the points on the right side of the point B is a ray. The arrow show that it can be extended without limit on its 1 sides. AB俗 differs from BA俗 It has a starting point and no ending point sowe cant measure its length. A B
- 9. Straight line ray Line segment AB is a subset of AB and AB is a subset of AB
- 10. What will happen if 2What will happen if 2 rays have the samerays have the same starting pointstarting point??
- 11. AB and AC are 2 rays having the same starting point A ..they made an angle A B C ) side ( )side( )the vertex of the angle(
- 12. The measuring of the angle: The angle is measured (by using the protractor( With degree unit) 属 ( The measure of ^BAC is written.. m (^BAC(
- 13. The type of angles: zero angle CA B Its measure = 0属 Its sides are coincident.
- 14. Acute angle A C B Its measure is more than 0属 and less than 90属 0属 < m (^BAC) < 90属
- 15. Right angle Its measure is 90属 m (^BAC) = 90属 B A C
- 16. Obtuse angle A C B Its measure is more than 90属 and less than 180属 90属 < m (^BAC) < 180属
- 17. Straight angle CAB Its measure is 180属 Its sides are forming one straight line. m (^BAC) = 180属
- 18. Reflex angle B A C Its measure is more than 18属 and less than 360属 180属 < m (^BAC) < 360属
- 19. Example: Mention the type of each of the angles which their measures are as follow 32属 90属 110属 180属 250属 159属
- 20. 32属 acute 90属 Right 110属 Obtuse 180属 straight 250属 reflex 159属 obtuse Solution:
- 22. Exercise: Define the type of each angle in the following shape 6 2 3 4 5 1 7
- 23. Try to solve them inTry to solve them in your note bookyour note book
- 24. H.W Work book p.26:Ex.1-20 And page 28
- 25. Miss Magda is proud of her students Excellent
- 26. 京霞艶b霞艶京霞艶b霞艶