   Chapter 2.5, Problem 30E ### 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: Quadrilateral ABCD with B A ¯ ⊥ A D ¯ and B C ¯ ⊥ D C ¯ Prove: ∠ s B and D are supplementary. To determine

To prove:

s B and D are supplementary.

Explanation

Given:

The following figure shows the given quadrilateral ABCD.

Approach:

(1) According to the definition of perpendicular, if XYYZ then mY=90°.

(2) The sum of measures of four angels in a quadrilateral is 360°.

(3) Angles will be supplementary if the sum of measures of two angles is 180°.

Calculation:

The proof is as follows.

 Proof Statements Reasons 1. BA¯⊥AD¯ and BC¯⊥DC¯ 1

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