Geometry For Enjoyment And Challenge
Geometry For Enjoyment And Challenge
91st Edition
ISBN: 9780866099653
Author: Richard Rhoad, George Milauskas, Robert Whipple
Publisher: McDougal Littell
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Chapter 6.3, Problem 9PSB
To determine

Prove that ΔRSV is isosceles.

Expert Solution & Answer
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Answer to Problem 9PSB

  ΔRSVisisosceles.

Explanation of Solution

Given information:

Given: f||g ; RTW is an isosceles Δ , with base TW¯

  Geometry For Enjoyment And Challenge, Chapter 6.3, Problem 9PSB , additional homework tip  1

Calculation

Consider the given figure,

  Geometry For Enjoyment And Challenge, Chapter 6.3, Problem 9PSB , additional homework tip  2

It is given that,

  f||g ; RTW is an isosceles Δ , with base TW¯

The legs of isosceles Δ are congruent.

  RT¯RW¯

The angles opposite to congruent sides are congruent,

  TW

We know that parallel lines determine a plane so,

  STWV is a plane

If a plane intersects two lines the lines are parallel.

  SV¯||TW¯

  RVSRWT[||linescorrespondinganglesareequal]RSTRTW[||linescorrespondinganglesareequal]

  RVSRWT[transitiveproperty]

The two angle s of a triangle are congruent opposite sides are congruent.

  RS¯RV¯

If a triangle has two congruent sides then it is isosceles.

  ΔRSVisisosceles.

Hence, proved ΔRSVisisosceles.

Chapter 6 Solutions

Geometry For Enjoyment And Challenge

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