   Chapter 2.1, Problem 26E ### 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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# Given: r ↔ ∥ s ↔ , r ⊥ t (See figure for Exercise 25 .) Prove: s ⊥ t

To determine

To check:

The given statement.

Explanation

Given:

The given statement is,

rs, t is transversal and rt.

Figure (1)

Concept:

If two lines are parallel to each other and cut by a transversal then the angles on the corresponding sides of the transversal are equal.

Approach:

The given statement is,

rs, t is transversal and rt.

m1=m2(Congruent because of corresponding angles)m2=90°

So,

st,

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

 Proof Statements Reasons 1. r∥s 1. Given 2.t is transversal 2. Given 3. r⊥t 3. Given 4. m∠1=90° 4. If the lines are perpendicular, then the angle is a right angle

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