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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 30 to 32, write a formal proof of each theorem.

If two parallel lines are cut by a transversal, then the pairs of exterior angles on the same sides of the transversal are supplementary.

To determine

To prove:

If two parallel lines are cut by a transversal, then the pairs of exterior angles on the same sides of the transversal are supplementary.

Explanation

Consider the below figure,

Figure (1)

ab, and c is transversal.

Properties used:

(1) If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.

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

Approach:

The proof for the given statement is shown in the following table,

Proof
Statements Reasons
1.ab 1. Given
2.c is transversal 2. Given
3.1537 3. If two parallel lines are cut by a transversal, then the corresponding angles are congruent.
4.5 and 3 are supplementary. 4. If two parallel lines are cut by a transversal, then the interior angles on the same side of the transversal are supplementary

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