Chapter 2.1, Problem 32E

Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Chapter
Section

Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

In Exercises 30 to 32, write a formal proof of each theorem.If a transversal is perpendicular to one of two parallel lines, then it is also perpendicular to the other line.

To determine

To prove:

If the transversal is perpendicular to one of two parallel lines, then it is also perpendicular to the other line.

Explanation

Consider the below figure,

Figure (1)

aâˆ¥b, c is transversal and aâŠ¥c.

Properties used:

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

Approach:

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

 Proof Statements Reasons 1.aâˆ¥b 1. Given 2.c is transversal 2. Given 3.aâŠ¥c 3. Given 4.âˆ 1 is a right angle. 4. If two lines are perpendicular to each then they are at right angles. 5.âˆ 2 is a right angle. 5. If two lines are perpendicular to each then they are at right angles. 6.âˆ 1â‰…âˆ 2 6. If two parallel lines are cut by a transversal, then the corresponding angles are congruent

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