Chapter 3.2, Problem 33E

### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

Chapter
Section

### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# Given: R W â†’ bisects âˆ  S R U Prove: R S Â¯ â‰… R U Â¯ Î” T R U â‰… Î” V R S (HINT: First show that Î” R S W â‰… Î” R U W .)

To determine

To prove:

The given statement.

Explanation

Given:

The given statements are,

RWâ†’ bisects âˆ SRU and RSÂ¯â‰…RUÂ¯

Figure (1)

Properties used:

(1) If two sides and the included angle between the sides of two triangles are equal, then the triangles are congruent.

(2) If two angles and one side of two triangles are equal, then the triangles are congruent.

(3) If two triangles are congruent to each other then all sides of the triangle are congruent.

Approach:

The first given statement is,

RWâ†’ bisects âˆ SRU

âˆ SRW and âˆ URW are the bisected angles.

So,

âˆ SRWâ‰…âˆ URW

The given statement is,

RSÂ¯â‰…RUÂ¯

The side RW is common in both triangles Î”MQP and Î”PNM.

So,

RWÂ¯â‰…RWÂ¯

Use SAS criteria of triangle congruency.

RSÂ¯â‰…RUÂ¯

âˆ SRWâ‰…âˆ URW

RWÂ¯â‰…RWÂ¯

So,

Î”RSWâ‰…Î”RUW

Use transitive property of congruence.

Î”RSWâ‰…Î”RUW and âˆ RSW, and âˆ RUW are the angles of congruent triangles

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