   Chapter 2.1, Problem 31E 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

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.a∥b 1. Given 2.c is transversal 2. Given 3.∠1≅∠5∠3≅∠7 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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