   Chapter 2.CT, Problem 16CT 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 16 and 18 , complete the missing statements or reasons for each proof. Given: ∠ 1 ≅ ∠ 2 ∠ 3 ≅ ∠ 4 Prove: l ∥ n PROOF Statements Reasons 1. ∠ 1 ≅ ∠ 2 ∠ 3 ≅ ∠ 4 1.               _ 2.               _ 2. If two lines intersect, the vertical ∠ s are ≅ 3. ∠ 1 ≅ ∠ 4 3.               _ 4.               _ 5. If two lines are cut by a transversal so that a pair of alternate exterior ∠ s are ≅ , the lines are ∥

To determine

To prove:

The given statement.

Explanation

Given:

The following figure shows the given diagram.

1234

Properties:

(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, 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.

Thus, 𝓁n.

 PROOF Statements Reasons 1.∠1≅∠2∠3≅∠4 1

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