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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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In Exercises 31 to 33, give a formal proof for each theorem.

If two lines are cut by a transversal so that a pair of exterior angles on the same side of the transversal are supplementary, then these lines are parallel.

To determine

To find:

The formal proof for the given theorem.

Explanation

Given:

Two lines 𝓁 and m are cut by a transversal t so that a pair of exterior angles on the same side of the transversal are supplementary.

Figure (1)

Theorem:

(1) If two lines are cut by a transversal so that two corresponding angles are congruent, then these lines are parallel.

(2) Angles on a straight line are supplementary.

Approach:

The given statement is,

Exterior angles 2 and 8 on the same side of the transversal t are supplementary.

So,

m2+m8=180°(1)

6 and 8 are supplementary angles.

So,

m6+m8=180°(2)

Subtract equation (2) from equation (1).

m2+m8m6m8=180°180°m2m6=0m2=m6

Therefore,

26

2 and 6 are congruent corresponding angles

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