   Chapter 2.4, Problem 30E ### 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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# Given: Equiangular Δ R S T Prove: R V → bisects ∠ S R T Δ R V S is a right Δ To determine

To prove:

ΔRVS is a right angle triangle or not.

Explanation

Given:

Equiangular ΔRST and RV¯ bisects ΔSRT.

Figure (1)

Approach:

The sum of interior angles of a triangle is equal to 180°.

Calculation:

mS+mT+mSRT=180°

mS+mSRV+mRVS=180°

Since, bisects SRT. Therefore,

mSRV=12(mSRT)

Since, ΔRST is an equiangular triangle. Therefore,

mS=mT

Consider, mS+mSRV

Substitute 12(mSRT) for mSRV, mT for mS, and 12(2mS) for mT.

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