   Chapter 2.3, 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 31 to 33, give a formal proof for each theorem.If two lines are cut by a transversal so that a pair of alternate exterior angles are congruent, 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 alternate exterior angles is congruent.

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) If two lines intersect, vertically opposite angles are congruent.

Approach:

The given statement is,

Alternate exterior angles are congruent.

27

2 and 3 are vertically opposite angles.

So,

32

And,

27

Use Transitive Property of congruence.

37

3 and 7 are congruent corresponding angles.

Thus, 𝓁m

The formal proof for the given theorem is shown in the following table.

 Proof Statements Reasons 1. ∠2≅∠7 1. Given 2. ∠3≅∠2 2

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