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The document discusses ways to prove that a quadrilateral is a parallelogram. There are 5 methods listed: 1) showing both pairs of opposite sides are parallel, 2) showing both pairs of opposite sides are congruent, 3) showing both pairs of opposite angles are congruent, 4) showing one pair of opposite sides are parallel and congruent, 5) showing the diagonals bisect each other. The document also mentions the homework assignment is to complete problems 4 through 20 on page 526 of the textbook, which are the even numbered problems.
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The document discusses ways to prove that a quadrilateral is a parallelogram. It lists five different theorems that can be used as proof: (1) showing both pairs of opposite sides are parallel, (2) showing both pairs of opposite sides are congruent, (3) showing both pairs of opposite angles are congruent, (4) showing one pair of opposite sides are parallel and congruent, (5) showing the diagonals bisect each other. The document provides examples of homework problems involving finding angle measures and side lengths that could be used to prove quadrilateral shapes are parallelograms.
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Triangles.pptx
1. There are four conditions that can be used to prove that two triangles are congruent: SAS, ASA, SSS, and RHS.
2. SAS means that two sides and the angle between them are equal in both triangles. ASA means that two angles and the side between them are equal. SSS means that all three sides are equal. RHS means that there is a right angle, equal hypotenuses, and one other equal side.
3. Some properties of triangles include: the angles opposite equal sides of an isosceles triangle are equal; the sides opposite equal angles are equal; and altitudes drawn to equal sides of a triangle are equal.
Summative assessment -I guess papers for class-ix
Grooming at the APEX INSTITUTE is done methodically focusing on understanding of the subject, tricks of tackling the questions and above all enthusing students with self confidence, ambition and a 'never say give up' spirit. As secrets of success these are no substitutes for hard work and patience.
Triangles ix
This document provides information about congruence of triangles from a geometry textbook. It includes definitions of congruent figures and associating real numbers with lengths and angles. It describes the one-to-one correspondence test for congruence of triangles. It discusses sufficient conditions for congruence including SAS, SSS, ASA, and SAA. It presents activities and examples verifying these tests and exploring properties of isosceles and equilateral triangles. The document encourages critical thinking through "Think it Over" prompts and upgrading the chapter with additional content.
Module 1 similarity
This module introduces ratio, proportion, and the Basic Proportionality Theorem. Students will learn about ratios, proportions, and how to use the fundamental law of proportions to solve problems involving similar triangles. The module is designed to help students apply the definition of proportion to find unknown lengths, illustrate and verify the Basic Proportionality Theorem and its converse, and develop skills for solving geometry problems involving triangles. Exercises cover writing and simplifying ratios, setting up and solving proportions, determining if ratios form proportions, and applying the Basic Proportionality Theorem.
8 1 and 8 2 second version.ppt
This document discusses ratios, proportions, and using them to solve problems. It defines a ratio as a comparison of two numbers using the same units, and can be written in simplified form. Proportions set two ratios equal and use the cross product property to solve for unknown values. Several examples demonstrate setting up and solving proportions for unknown side lengths of shapes and unknown values in expressions using properties of ratios and proportions.
8 1 and 8 2 second version.ppt
This document discusses ratios, proportions, and using them to solve problems. It defines a ratio as a comparison of two numbers using the same units, and can be written in simplified form. Proportions set two ratios equal and use the cross product property to solve for unknown values. Several examples demonstrate setting up and solving proportions for unknown side lengths of shapes and unknown values in expressions involving ratios.
1. ejercicios
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9 std Triangles.pptx
This document contains geometry problems and exercises about triangles. It includes problems about congruent triangles, isosceles triangles, right triangles, and relationships between sides and angles. The document provides 8 problems for students to work through regarding criteria for triangle congruence. It then lists 8 additional exercises involving properties of isosceles triangles and relationships in various triangle configurations.
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