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Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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Chapter
Section
BuyFindarrow_forward

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 each parallel to the same line, then these lines are parallel to each other. (Assume three coplanar lines.)

To determine

To find:

The formal proof for the given theorem.

Explanation

Given:

Two lines w and y are each parallel to the same line x.

Figure (1)

Theorem:

If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.

Approach:

Line w is parallel to line x.

So,

12

Line y is parallel to line x.

So,

23

Use Transitive Property of congruence.

13

1 and 3 are corresponding congruent angles.

Thus, line w is parallel to y.

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

Proof
Statements Reasons
1. wx 1. Given
2. yx 2. Given
3. 12 and 23 3. If two lines are cut by a transversal, then the corresponding s are
4

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