Q9. In Exercises 9 and 10 you are gi... [FREE SOLUTION]

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 4: Q9. (page 131)

In Exercises 9 and 10 you are given more information than you need. For each exercise state one piece of given information that you do not need for the proof. Then give a two鈥揷olumn proof that does not use that piece of information.
Given: $\overset{炉}{P Q} 鈮� \overset{炉}{P S}; \overset{炉}{Q R} 鈮� \overset{炉}{S R}; 鈭� 1 鈮� 鈭� 2$
Prove: $鈭� 3 鈮� 鈭� 4$

Expert verified

$鈭� 1 鈮� 鈭� 2$ is not needed in given information to give proof.

Statement	Reason
1. $\overset{炉}{P Q} 鈮� \overset{炉}{P S}$	Given
2. $\overset{炉}{P R} 鈮� \overset{炉}{P R}$	Given
3. $\overset{炉}{Q R} 鈮� \overset{炉}{S R}$	Given
4. $螖 P Q R 鈮� 螖 P S R$	SSS congruency criteria
5. $鈭� 3 鈮� 鈭� 4$	corresponding parts of congruent triangle are congruent

Since, line segment $\overset{炉}{P R}$ is common to both triangles, by relexive property it is congruent to itself

So, $\overset{炉}{P R} 鈮� \overset{炉}{P R}$

From step 1 using given statement $螖 P Q R 鈮� 螖 P S R$ by SSS (Side-Side-Side) congruency criteria

Since, corresponding parts of congruent triangle are congruent

Thus, $鈭� 3 鈮� 鈭� 4$

Also proof is provided without using $鈭� 1 鈮� 鈭� 2$ , so it is not needed in given information.

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