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Elementary Geometry for College St...

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

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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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Given: m 2 + m 3 = 90 °
B E ¯ bisects A B C
C E ¯ bisects B C D
Prove: l n

Chapter 2.3, Problem 38E, Given: m2+m3=90 BE bisects ABC CE bisects BCD Prove: ln

To determine

To prove:

The line l is parallel to line m.

Explanation

Given:

The given statements are,

m2+m3=90°

BE¯ bisects ABC and CE¯ bisects BCD.

Figure (1)

Property:

(1) If two lines are cut by a transversal so that two interior angles on the same side of the transversal are supplementary, then these lines are parallel.

(2) Supplementary angles add up to 180°.

Approach:

The given statement is,

m2+m3=90°(1)

BE¯ bisects ABC and CE¯ bisects BCD.

m2=m1m3=m4

Substitute m1 for m2 and m4 for m3 in equation (1)

m1+m4=90°(2)

Add equation (1) and equation (2).

m2+m3+m1+m4=90°+90°m1+m2+m3+m4=180°mABC+mBCD=180°

ABC and BCD are two interior angles on the same side of the transversal which are supplementary.

So, 𝓁m.

The complete proof is shown in the following statement

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