   Chapter 2.4, Problem 30E 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: 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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