Geometry is an important branch of mathematics that deals with shapes, sizes, and properties of space. One of the fundamental concepts in geometry is congruent triangles, which are triangles that have the same size and shape. In Unit 4 of a geometry course, students are introduced to the concept of congruent triangles and are given homework assignments to reinforce their understanding of the topic. This article aims to provide a comprehensive answer key for Unit 4 Congruent Triangles Homework 3 to assist students in checking their work and understanding the correct solutions to the problems.
Understanding Congruent Triangles
Congruent triangles are triangles that have the same size and shape. They can be superimposed onto each other, and their corresponding sides and angles are equal. There are several methods to prove that triangles are congruent, such as using the side-angle-side (SAS), angle-side-angle (ASA), side-side-side (SSS), angle-angle-side (AAS), and hypotenuse-leg (HL) congruence criteria.
Importance of Homework 3 in Unit 4
Homework 3 in Unit 4 of a geometry course focuses on applying the concepts of congruent triangles to solve problems. This homework helps students practice identifying congruent parts of triangles, proving that triangles are congruent based on given information, and using congruent triangles to solve real-world problems. It is crucial for students to have a thorough understanding of these concepts as they form the basis for more advanced topics in geometry and other branches of mathematics.
The Answer Key for Homework 3
Below is the comprehensive answer key for Unit 4 Congruent Triangles Homework 3:
- Problem 1: Given triangle ABC and triangle DEF, where angle A = angle D, angle B = angle E, and AB = DE. Prove that triangle ABC is congruent to triangle DEF using the ASA congruence criterion.
- Problem 2: In triangle XYZ, angle X = 70 degrees, angle Y = 50 degrees, and segment XY = segment YZ. Find the measure of angle Z.
Solution: To prove that triangle ABC is congruent to triangle DEF using the ASA congruence criterion, we need to show that angle A = angle D, angle B = angle E, and segment AB = segment DE. First, we can use the given information that angle A = angle D and angle B = angle E. Then, using the given information that AB = DE, we can conclude that triangle ABC is congruent to triangle DEF by the ASA congruence criterion.
Solution: Since segment XY = segment YZ, we can conclude that triangle XYZ is isosceles. Therefore, angle Y = angle Z. Using the given information that angle X = 70 degrees and angle Y = 50 degrees, we can find the measure of angle Z by subtracting the sum of angles X and Y from 180 degrees. Hence, angle Z = 180 – (70 + 50) = 60 degrees.
Conclusion
Unit 4 Congruent Triangles Homework 3 is a crucial part of a geometry course, and having a comprehensive answer key can greatly aid students in understanding and checking their work. By mastering the concepts of congruent triangles and successfully completing the homework assignments, students will be well-prepared for more advanced topics in geometry and other branches of mathematics.
