   Chapter 6.1, Problem 32E ### Elementary Geometry for College St...

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

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# In Exercises 32 to 37, write a paragraph proof. Given: R S ¯  and  T V ¯  are diameters of  ⊙ W Prove: Δ R S T ≅ Δ V T S To determine

To prove:

A paragraph proof when RS¯ and TV¯ are diameters of W then ΔRSTΔVTS.

Explanation

Given:

The line segments RS¯ and TV¯ are diameters of W.

Rule used:

SAS congruency rule:

If two sides and the included angle of one triangle are equal to two sides and included angle of another triangle, then the triangles are congruent.

SSS congruency rule:

If three sides of one triangle are equal to three sides of another triangle then the triangles are congruent.

Proof:

Let RS¯ and TV¯ be the diameters of circle W.

Since all the diameters of the circle are of same length, RS¯TV¯.

Also, all the radii of the circle are of same length, WR¯WV¯ and WT¯WS¯.

From the figure, we see that the diameters RS¯ and TV¯ form vertical angles, which are congruent

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