   Chapter 2.3, Problem 18E ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# In Exercises 17 and 18 , complete each proof by filling in the missing statements and reasons. Given: l ∥ m ∠ 3 ≅ ∠ 4 Prove: l ∥ n PROOF Statements Reasons 1. l ∥ m 1. ? 2. ∠ 1 ≅ ∠ 2 2. ? 3. ∠ 2 ≅ ∠ 3 3. If two lines intersect, the vertical ∠ s formed are ≅ 4. ? 4. Given 5. ∠ 1 ≅ ∠ 4 5. Transitive Property of ≅ 6. ? 6. ?

To determine

To fill:

The missing statements in the given table.

Explanation

Given:

The given statement is,

𝓁m and 34

Figure (1)

Properties used:

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

(2) If two lines intersect, then the vertically opposite angles formed are congruent.

Approach:

The first given statement is,

𝓁m

Line 𝓁 and line m are parallel lines and 1 and 2 are corresponding angles.

So,

12

2 and 3 are vertically opposite angles.

So,

23

Now, 12 and 23.

Use transitive property of congruence.

13

The given statement is,

34

Again, use transitive property of congruence.

14

1 and 4 are congruent corresponding angles

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