Quads factored form updated with answers jbianco9910
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Turn in homework on the bookshelf and complete algebra problems 15-18 from the packet. The summary discusses the factored form of a quadratic equation as y=a(x+b)(x+c) or f(x)=a(x+b)(x+c), where a determines if the parabola opens up or down and the opposite values of b and c represent the x-intercepts of the equation.
1004 review of postualtes definitions etcjbianco9910
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Put your homework on the corner of your desk. The same seats will be used in Geometry class today where students will review definitions and postulates for opposite rays and non-opposite rays as part of Drill #3.
The document provides instructions for an algebra drill session. Students are told to silently complete a worksheet taken from the book shelf, having their homework on the corner of their desk. The worksheet contains questions about interpreting points on scatter plots, writing equations for lines of best fit, and identifying the type of relationship (positive, negative, or none) shown in different scatter plots.
This algebra lesson discusses plotting points on a Cartesian plane using a rule to generate the points. Students will analyze graphs to generalize function families and write algebraic equations to describe the graphs and rules. They will evaluate functions for domain values and solve functions given range values. The lesson instructs students to begin an assignment with partners and homework.
5002 more with perp and angle bisector and cea updatedjbianco9910
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Students were instructed to place their homework from the previous Wednesday on their desk and turn in any unfinished work from the prior Friday. They were then told to copy geometry questions and self-assess their answers as a guess, unsure, or sure. The objective was for students to review properties of perpendicular bisectors, angle bisectors, and demonstrate what they have learned in honors geometry over the course of the year.
The document discusses geometry concepts related to triangles including medians, altitudes, centroids, and orthocenters. It defines key terms such as median, altitude, centroid, and orthocenter. It also explains that the medians and altitudes of a triangle are concurrent and intersect at specific points, namely the centroid and orthocenter.
1) The document discusses properties of similar right triangles, including that the altitude to the hypotenuse divides the triangle into two similar triangles.
2) It defines the geometric mean and provides examples of finding the geometric mean between pairs of numbers.
3) The document explains that the ratio of the longer legs is equal to the ratio of the shorter legs, known as the "Long-Long, Short-Short" property.
The document discusses simulations that can be used to determine probabilities of random events. It provides examples of using tools like coins, dice, and random number generators with specific rules to simulate probabilities. It also gives directions to design simulations for scenarios involving the chances of rain in Spain, admissions at Hershey Park, family sizes, and students with pets.
Chapter 5 unit f 003 review and more updatedjbianco9910
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The document provides instructions and diagrams for 4 math problems involving angles and perpendicular bisectors. It aims to review skills around finding unknown angles and distances given information about perpendicular or angle bisectors. The final section models explaining geometric proofs through stating reasons and using theorems such as vertical angles, alternate interior angles, and angle-angle-side.
The document provides instruction on classifying triangles and the Pythagorean theorem. It defines right triangles as having one 90 degree angle and defines the legs and hypotenuse. It presents the Pythagorean theorem that the sum of the squares of the two legs equals the square of the hypotenuse. It also provides corollaries that an acute triangle has the sum of the leg squares less than the hypotenuse square, an obtuse triangle has the sum greater than the hypotenuse square, and a right triangle has the sums equal. It asks students to classify triangles as acute, obtuse or right using the corollaries and Pythagorean theorem.
You will need your construction tools to copy segments and angles from GEOM Drill 2.12. There are three ways to prove triangles are congruent: the Side-Side-Side Postulate (SSS), the Side-Angle-Side Postulate (SAS), and the Angle-Side-Angle Postulate (ASA). To use these postulates, you must measure either three sides, two sides and the included angle, or two angles and the included side of two triangles.
1. The document discusses geometric concepts related to polyhedrons including prisms. It defines key terms like polyhedron, lateral area, surface area, altitude, net, prism, right prism, and provides formulas to calculate lateral area and surface area of right prisms.
2. Examples are given to identify 3D shapes from their nets and to draw orthographic views of objects. The document also contains classwork on drawing nets and calculating measurements of prisms.
3. Geometric concepts like polyhedrons, prisms, lateral area, surface area, and orthographic views are defined and formulas/examples are provided for calculating measurements and drawing representations of prisms.
Parralelogram day 1 with answersupdated jbianco9910
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A parallelogram is a quadrilateral with two pairs of parallel sides. Students were assigned geometry homework to find the values of x and y in figures and provide proof of their answers, placing their homework and pen on the corner of their desk. They were asked to define a parallelogram.
1. The document provides definitions and theorems about right triangles, including the Pythagorean theorem. It defines the legs and hypotenuse of a right triangle, and states that the sum of the squares of the two legs equals the square of the hypotenuse.
2. It also describes a corollary to the Pythagorean theorem, stating that if the sum of the squares of the two shorter sides is less than the square of the longest side, the triangle is obtuse, if the sum is greater it is acute, and if the sum is equal the triangle is right.
3. Examples are given to classify triangles as right, obtuse or acute using this corollary to the Pythagorean
The document contains notes from a geometry drill on identifying parallelograms and determining values of x and y in parallelogram figures. It lists homework answers and a classwork assignment to identify parallelograms from figures and state the relevant definition or theorem, as well as an assignment to complete 15 problems showing work.
The document contains instructions and content for a geometry drill lesson. The objective is for students to discover properties of special parallelograms. The lesson includes definitions and examples of rectangles, rhombi, squares, and parallelograms. Students are asked to identify these shapes in diagrams and list their defining properties. They will also complete problems finding missing side lengths and plotting point coordinates to identify geometric objects.
1. The document provides geometry problems involving calculating interior and exterior angle measures of various regular and non-regular polygons. It asks students to find angle sums and individual angle measures for polygons with a specified number of sides.
2. Questions involve calculating interior and exterior angle sums and measures for polygons ranging from pentagons to 15-gons and up to polygons with 30 or 36 sides. Students are asked to determine properties of polygons like the number of sides if the interior angle sum is given.
The document provides instructions to complete geometry homework problems involving regular polygons, parallelograms, and finding missing angle measures. Students are asked to find: the number of sides of two regular polygons given interior and exterior angle measures; angle measures and that parallelogram EFGH is a parallelogram; angle measures x, y, and z for two parallelograms; and to show work for problems 8 through 10.
The document outlines a geometry drill session that reviews special right triangles and chapter 5 material. It provides several problems to find missing sides of right triangles given certain measurements, instructing students to show their work and use formulas. Problems include finding sides of triangles with angles of 30-60-90, 45-45-90, and solving for unknown sides using trigonometric ratios.
Pytha drill into lines of concurrency day 2jbianco9910
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This document contains notes from a geometry lesson on using properties of perpendicular bisectors, angle bisectors, midsegments, and medians of a triangle. It includes three examples of using perpendicular bisectors and angle bisectors to find distances in triangles. It also poses a question about what geometric construction could be used to find a location equal distance from three given points X, Y, and Z, which represents finding the circumcenter of a triangle formed by those points.
1) The document provides instructions for an honors geometry class, including having homework and a pen ready, an upcoming quiz on Friday, and drill problems to work on finding missing side lengths of triangles using properties like the Pythagorean theorem.
2) Students are asked to work with a partner using devices and packets to investigate triangle properties like perpendicular bisectors, angle bisectors, midsegments, and medians using geometry software.
3) Key vocabulary is defined, like what a midsegment of a triangle is and the midsegment theorem. Sample problems are provided applying these concepts.
Students were assigned homework involving triangles and the Pythagorean theorem due on February 8th. The objective of the assignment was for students to review the triangle inequality theorem and Pythagorean theorem as it relates to triangles.
5002 more with perp and angle bisector and ceajbianco9910
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Students were instructed to place their homework from the previous Wednesday on their desk and turn in any unfinished work from the prior Friday. They were then told to copy geometry questions and self-assess their answers as a guess, unsure, or sure. The objective was to review properties of perpendicular bisectors, angle bisectors, and demonstrate what students have learned over the course of the year.
This document provides definitions, examples, and practice problems related to perpendicular bisectors and angle bisectors. It begins by defining perpendicular bisectors as the locus of points equidistant from the endpoints of a segment. Angle bisectors are defined as the locus of points equidistant from the sides of an angle. Examples show applying theorems about perpendicular and angle bisectors to find missing measures. The document concludes with an example writing an equation for a perpendicular bisector in point-slope form.
The document discusses simulations that can be used to determine probabilities of random events. It provides examples of using tools like coins, dice, and random number generators with specific rules to simulate probabilities. It also gives directions to design simulations for scenarios involving the chances of rain in Spain, admissions at Hershey Park, family sizes, and students with pets.
Chapter 5 unit f 003 review and more updatedjbianco9910
Ìý
The document provides instructions and diagrams for 4 math problems involving angles and perpendicular bisectors. It aims to review skills around finding unknown angles and distances given information about perpendicular or angle bisectors. The final section models explaining geometric proofs through stating reasons and using theorems such as vertical angles, alternate interior angles, and angle-angle-side.
The document provides instruction on classifying triangles and the Pythagorean theorem. It defines right triangles as having one 90 degree angle and defines the legs and hypotenuse. It presents the Pythagorean theorem that the sum of the squares of the two legs equals the square of the hypotenuse. It also provides corollaries that an acute triangle has the sum of the leg squares less than the hypotenuse square, an obtuse triangle has the sum greater than the hypotenuse square, and a right triangle has the sums equal. It asks students to classify triangles as acute, obtuse or right using the corollaries and Pythagorean theorem.
You will need your construction tools to copy segments and angles from GEOM Drill 2.12. There are three ways to prove triangles are congruent: the Side-Side-Side Postulate (SSS), the Side-Angle-Side Postulate (SAS), and the Angle-Side-Angle Postulate (ASA). To use these postulates, you must measure either three sides, two sides and the included angle, or two angles and the included side of two triangles.
1. The document discusses geometric concepts related to polyhedrons including prisms. It defines key terms like polyhedron, lateral area, surface area, altitude, net, prism, right prism, and provides formulas to calculate lateral area and surface area of right prisms.
2. Examples are given to identify 3D shapes from their nets and to draw orthographic views of objects. The document also contains classwork on drawing nets and calculating measurements of prisms.
3. Geometric concepts like polyhedrons, prisms, lateral area, surface area, and orthographic views are defined and formulas/examples are provided for calculating measurements and drawing representations of prisms.
Parralelogram day 1 with answersupdated jbianco9910
Ìý
A parallelogram is a quadrilateral with two pairs of parallel sides. Students were assigned geometry homework to find the values of x and y in figures and provide proof of their answers, placing their homework and pen on the corner of their desk. They were asked to define a parallelogram.
1. The document provides definitions and theorems about right triangles, including the Pythagorean theorem. It defines the legs and hypotenuse of a right triangle, and states that the sum of the squares of the two legs equals the square of the hypotenuse.
2. It also describes a corollary to the Pythagorean theorem, stating that if the sum of the squares of the two shorter sides is less than the square of the longest side, the triangle is obtuse, if the sum is greater it is acute, and if the sum is equal the triangle is right.
3. Examples are given to classify triangles as right, obtuse or acute using this corollary to the Pythagorean
The document contains notes from a geometry drill on identifying parallelograms and determining values of x and y in parallelogram figures. It lists homework answers and a classwork assignment to identify parallelograms from figures and state the relevant definition or theorem, as well as an assignment to complete 15 problems showing work.
The document contains instructions and content for a geometry drill lesson. The objective is for students to discover properties of special parallelograms. The lesson includes definitions and examples of rectangles, rhombi, squares, and parallelograms. Students are asked to identify these shapes in diagrams and list their defining properties. They will also complete problems finding missing side lengths and plotting point coordinates to identify geometric objects.
1. The document provides geometry problems involving calculating interior and exterior angle measures of various regular and non-regular polygons. It asks students to find angle sums and individual angle measures for polygons with a specified number of sides.
2. Questions involve calculating interior and exterior angle sums and measures for polygons ranging from pentagons to 15-gons and up to polygons with 30 or 36 sides. Students are asked to determine properties of polygons like the number of sides if the interior angle sum is given.
The document provides instructions to complete geometry homework problems involving regular polygons, parallelograms, and finding missing angle measures. Students are asked to find: the number of sides of two regular polygons given interior and exterior angle measures; angle measures and that parallelogram EFGH is a parallelogram; angle measures x, y, and z for two parallelograms; and to show work for problems 8 through 10.
The document outlines a geometry drill session that reviews special right triangles and chapter 5 material. It provides several problems to find missing sides of right triangles given certain measurements, instructing students to show their work and use formulas. Problems include finding sides of triangles with angles of 30-60-90, 45-45-90, and solving for unknown sides using trigonometric ratios.
Pytha drill into lines of concurrency day 2jbianco9910
Ìý
This document contains notes from a geometry lesson on using properties of perpendicular bisectors, angle bisectors, midsegments, and medians of a triangle. It includes three examples of using perpendicular bisectors and angle bisectors to find distances in triangles. It also poses a question about what geometric construction could be used to find a location equal distance from three given points X, Y, and Z, which represents finding the circumcenter of a triangle formed by those points.
1) The document provides instructions for an honors geometry class, including having homework and a pen ready, an upcoming quiz on Friday, and drill problems to work on finding missing side lengths of triangles using properties like the Pythagorean theorem.
2) Students are asked to work with a partner using devices and packets to investigate triangle properties like perpendicular bisectors, angle bisectors, midsegments, and medians using geometry software.
3) Key vocabulary is defined, like what a midsegment of a triangle is and the midsegment theorem. Sample problems are provided applying these concepts.
Students were assigned homework involving triangles and the Pythagorean theorem due on February 8th. The objective of the assignment was for students to review the triangle inequality theorem and Pythagorean theorem as it relates to triangles.
5002 more with perp and angle bisector and ceajbianco9910
Ìý
Students were instructed to place their homework from the previous Wednesday on their desk and turn in any unfinished work from the prior Friday. They were then told to copy geometry questions and self-assess their answers as a guess, unsure, or sure. The objective was to review properties of perpendicular bisectors, angle bisectors, and demonstrate what students have learned over the course of the year.
This document provides definitions, examples, and practice problems related to perpendicular bisectors and angle bisectors. It begins by defining perpendicular bisectors as the locus of points equidistant from the endpoints of a segment. Angle bisectors are defined as the locus of points equidistant from the sides of an angle. Examples show applying theorems about perpendicular and angle bisectors to find missing measures. The document concludes with an example writing an equation for a perpendicular bisector in point-slope form.
The document provides instructions for students to complete a geometry handout individually. It asks students to draw a segment 8 inches long labeled AB, draw a right angle from point A, mark off 6 inches from point A to point C to form a right triangle, and connect points B and C. It then asks students whether the resulting triangles would be congruent for everyone and why or why not. The document also states the objective is to review for a geometry test on Friday and includes blanks for stating geometry statements, reasons, and constructing proofs.
This document provides lesson materials on isosceles and equilateral triangles including:
- Key vocabulary terms like legs, vertex angle, and base of an isosceles triangle.
- The Isosceles Triangle Theorem and its converse.
- Properties and theorems regarding equilateral triangles.
- Examples proving triangles congruent using corresponding parts of congruent triangles (CPCTC).
- A lesson quiz to assess understanding of isosceles triangle properties and angle measures.
Chapter4006more with proving traingle congruentjbianco9910
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The document contains notes from a geometry class, including examples of proofs of triangle congruence using various postulates and theorems. Several triangle congruence proofs are shown using criteria such as ASA, SAS, and SSS. Key vocabulary terms like hypotenuse and legs are defined. The Pythagorean theorem and its formula are stated.
This document contains information about proving triangles congruent using various postulates and theorems of geometry including:
- SSS (side-side-side) postulate
- SAS (side-angle-side) postulate
- ASA (angle-side-angle) postulate
- AAS (angle-angle-side) theorem
- Hypotenuse-Leg theorem
It also defines key terms like hypotenuse and legs of a right triangle and presents the Pythagorean theorem.
The document provides examples and explanations of congruent triangles. It begins with warm up questions about naming sides and angles of a triangle. It then discusses how to prove triangles are congruent using corresponding angles and sides being equal. Several examples are provided of using properties of congruent triangles to find missing angle measures or side lengths. Diagrams are included to illustrate bisectors and midpoints used in proofs of triangle congruence.
This document is from a geometry textbook. It discusses classifying triangles based on their angle measures and side lengths. There are examples of classifying triangles as acute, obtuse, right, equiangular, isosceles, scalene, and equilateral. It also discusses finding missing angle measures and side lengths using triangle properties and theorems like the Triangle Sum Theorem.