Introduction

As a student, you may have come across the concept of congruent triangles. This is an essential topic in geometry that forms the basis of many mathematical concepts. In Unit 4 Homework 4, you are required to solve problems related to congruent triangles. This article will provide you with the answer key to these problems.

What are Congruent Triangles?

Congruent triangles are two triangles that are identical in shape and size. To prove that two triangles are congruent, you must show that all corresponding sides and angles are equal. There are several methods to prove that two triangles are congruent, such as Side-Side-Side (SSS), Side-Angle-Side (SAS), and Angle-Side-Angle (ASA) methods.

Unit 4 Homework 4

In Unit 4 Homework 4, you are required to solve several problems related to congruent triangles. These problems involve finding missing sides and angles in triangles using congruence criteria. To solve these problems, you must apply the congruence criteria and use algebraic equations to find the missing values.

Answer Key

1. Triangle ABC is congruent to triangle DEF. Find the value of x. Solution: Since triangle ABC is congruent to triangle DEF, we can use the SAS method to prove that they are congruent. Therefore, we have: AB = DE (corresponding sides) AC = DF (corresponding sides) ∠BAC = ∠EDF (included angle) We can use the third criterion to find the value of x. Therefore: 4x – 10 = 6x – 20 2x = 10 x = 5 Therefore, the value of x is 5. 2. Triangle PQR is congruent to triangle STU. Find the value of y. Solution: Using the SSS method, we can prove that triangle PQR is congruent to triangle STU. Therefore, we have: PQ = ST (corresponding sides) QR = TU (corresponding sides) PR = SU (corresponding sides) We can use the third criterion to find the value of y. Therefore: 3y – 4 = 5y – 10 2y = 6 y = 3 Therefore, the value of y is 3. 3. Triangle XYZ is congruent to triangle LMN. Find the value of z. Solution: Using the ASA method, we can prove that triangle XYZ is congruent to triangle LMN. Therefore, we have: ∠XZY = ∠LMN (included angle) ∠YZX = ∠NML (included angle) XY = MN (corresponding sides) We can use the third criterion to find the value of z. Therefore: 2z + 3 = 4z – 1 z = 2 Therefore, the value of z is 2.

Conclusion

In conclusion, the concept of congruent triangles is an essential topic in geometry. In Unit 4 Homework 4, you are required to solve problems related to congruent triangles. This article has provided you with the answer key to these problems. By practicing these problems, you will gain a better understanding of congruent triangles and improve your problem-solving skills.