   Chapter 5.2, Problem 36E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Given △ R S T , a second triangle ( △ U V W ) is constructed so that U V = 2 ( R S ) , V W = 2 ( S T ) , and W U = 2 ( R T ) . a) What is the constant value of the ratios U V R S , V W S T , W U R T ? b) Using intuition (appearance), does it seem that △ U V W is similar to △ R S T ? To determine

a)

The constant value of the ratios UVRS,VWST,and WURT.

Explanation

Definition:

Similarity between Two polygons:

Two polygons are similar if and only if when all pairs of corresponding angles are congruent and all pairs of corresponding sides are proportional

Given:

It is given that UV=2(RS),VW=2(ST),and WU=2(RT).

Calculation:

Divide by RS in both side of the equation UV=2(RS), we get

UVRS=2(RS)RS=2

Divide by ST in both side of the equation VW=2(ST), we get

To determine

b)

Whether it seems that ΔUVW is similar to ΔRST.

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