   Chapter 2.3, Problem 21E 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 Exercise 19 to 22 complete the proof. Given: D E → bisects ∠ C D A ∠ 3 ≅ ∠ 1 Prove: E D ¯ ∥ A B ¯ To determine

To find:

The complete proof for the given statement.

Explanation

Given:

The given statement is,

DE bisects CDA and 31.

Figure (1)

Theorem:

If two lines are cut by a transversal so that alternate interior angles are congruent, then these lines are parallel.

Approach:

The given statement is,

DE bisects CDA and 31.

Therefore,

23

Use Transitive Property of congruence.

21

1 and 2 are two congruent alternate interior angles.

Thus, ED¯AB¯.

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

 Proof Statements Reasons 1. ∠2≅∠3 1. DE→ bisects ∠CDA 2. ∠3≅∠1 2

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