   Chapter 2.1, Problem 22E 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

Given: l ∥ m   and   m ∥ n Prove: ∠ 1 ≅ ∠ 4 PROOF Statements Reasons 1. l ∥ m 1. ? 2. ∠ 1 ≅ ∠ 2 2.? 3. ∠ 2 ≅ ∠ 3 3. ? 4. ? 4. Given 5. ∠ 3 ≅ ∠ 4 5. ? 6. ? 6. ? To determine

To check:

Whether 1 is congruent to 4 or not.

Explanation

Given:

The given statement is,

𝓁mandmn

Figure (1)

Properties used:

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

(2) Vertically opposite angles are congruent to each other.

Approach:

The proof of the given statement is shown in the following table:

 Proof Statements Reasons 1. 𝓁∥m 1. Given 2. ∠1≅∠2 2. If two ∥ are cut by transversal, then the pair of corresponding ∠ s are congruent. 3. ∠2≅∠3 3. Vertically opposite angles. 4. m∥n 4. Given 5. ∠3≅∠4 5

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