The document contains geometry problems and questions about triangle properties including:
1) Finding missing side lengths of triangles given other side lengths.
2) Determining triangle types based on given side lengths.
3) Finding the length of a leg of a right triangle when the hypotenuse and one leg are given.
4) Finding the length of the longer leg of a 30-60-90 triangle when the longest side is given.
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.
This geometry lesson covered writing and graphing lines, classifying lines as parallel, intersecting, or coinciding, and using slope-intercept and point-slope forms of linear equations. Key concepts included using the slope formula, interpreting slope as a rate of change, and caution that four given points do not always determine two lines. Students were assigned practice problems and notified of an upcoming chapter test.
This document discusses properties of parallelograms. It defines a parallelogram as a quadrilateral with two pairs of parallel sides. The document proves several properties of parallelograms, including that opposite sides are congruent and opposite angles are congruent. It provides examples of using these properties to find missing side lengths and angle measures in parallelograms.
The document contains instructions and problems for geometry class. It includes 9 multiple choice and short answer questions about finding lengths, coordinates, measures, and averages in various triangles. It concludes by asking students to make a conjecture about the centroid of a triangle based on finding the average of the x- and y-coordinates of triangle vertices.
Given a bag with 40 marbles total, with 12 blue, 5 red, 9 green, and 14 yellow, the probability that the second marble drawn is blue, given that the first was green, is 12/34.
Given a box with 50 cards total, with 20 sixth graders, 16 seventh graders, and 14 eighth graders, and the first two cards drawn were sixth graders, the probability that the third card drawn is an eighth grader is 14/28.
Given a bag with 5 red apples, 7 yellow apples, and 8 green apples, the probability that Brett picks a green apple is 8/20.
1) The document provides instructions and examples for working with special right triangles and the Pythagorean theorem. It includes examples of finding missing sides of 30-60-90 and 45-45-90 triangles.
2) There are 4 problems that ask the reader to find missing sides (labeled z and y) of triangles where some measurements are given. Diagrams illustrate each triangle.
3) Formulas are provided for finding missing sides of 30-60-90 and 45-45-90 triangles based on a given shorter side.
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.
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.
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 examples of calculating lateral area and surface area of right prisms.
2. Examples are given of identifying 3D shapes from their nets and drawing orthographic views of objects. Formulas are provided for finding the lateral area and surface area of right prisms given the height and parameters of the base.
3. The document is a lesson on geometric concepts involving polyhedrons, prisms, nets, lateral area, surface area, and includes examples and practice problems for students.
The document discusses the Isosceles Triangle Theorem and its converse. It defines an isosceles triangle as a triangle with two congruent sides. The Isosceles Triangle Theorem states that if two sides of a triangle are congruent, then the angles opposite those sides are also congruent. The converse states that if two angles of a triangle are congruent, then the sides opposite those angles must be congruent. The document asks questions about bisecting vertex angles and finding missing angles and sides of isosceles triangles.
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 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.
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.
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.
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.
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.
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.
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.
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.
5002 more with perp and angle bisector and cea updatedjbianco9910
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 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.
Chapter4006more with proving traingle congruentjbianco9910
Ìý
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.
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.
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 examples of calculating lateral area and surface area of right prisms.
2. Examples are given of identifying 3D shapes from their nets and drawing orthographic views of objects. Formulas are provided for finding the lateral area and surface area of right prisms given the height and parameters of the base.
3. The document is a lesson on geometric concepts involving polyhedrons, prisms, nets, lateral area, surface area, and includes examples and practice problems for students.
The document discusses the Isosceles Triangle Theorem and its converse. It defines an isosceles triangle as a triangle with two congruent sides. The Isosceles Triangle Theorem states that if two sides of a triangle are congruent, then the angles opposite those sides are also congruent. The converse states that if two angles of a triangle are congruent, then the sides opposite those angles must be congruent. The document asks questions about bisecting vertex angles and finding missing angles and sides of isosceles triangles.
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 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.
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.
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.
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.
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.
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.
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.
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.
5002 more with perp and angle bisector and cea updatedjbianco9910
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 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.
Chapter4006more with proving traingle congruentjbianco9910
Ìý
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.
1. The document contains an honors geometry drill with 11 problems. The problems involve identifying angle theorems/postulates, finding unknown angle measures, naming parallel/perpendicular relationships, writing inequalities, solving equations, and completing a two-column proof.
2. The first 4 problems require stating the angle theorem and finding unknown angle measures using properties of alternate interior/exterior angles, corresponding angles, and same-side interior angles.
3. Problems 5-8 require naming the angle theorem that proves lines are parallel or perpendicular. The final problems involve an inequality, solving an equation, and completing a two-column proof.
1. The document contains instructions and examples for a geometry drill on lines and linear equations. Students are told to put their homework on the corner of their desk and that the drill will cover finding slope, writing and graphing lines in slope-intercept and point-slope form, and classifying lines as parallel, intersecting, or coinciding.
2. The warm-up problems involve substituting values into the equation y=mx+b to solve for b and solving linear equations for y. The objectives are listed as graphing lines and writing their equations in slope-intercept and point-slope form.
3. Students are reminded that a line's y-intercept is the b value in y=mx+