   Chapter 4.2, Problem 27E ### 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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# In Exercises 25 to 28, write a formal proof of each theorem or corollary.In a kite, one diagonal is the perpendicular bisector of the other diagonal.

To determine

A formal proof of the theorem ‘In a kite, one diagonal is the perpendicular bisector of the other diagonal’.

Explanation

Formal proof,

Statement:

In a kite, one diagonal is the perpendicular bisector of the other diagonal.

Drawing:

Given:

ABCD is a kite with diagonals AC and BD which intersect at ‘O’.

Prove:

AC¯BD¯

OA¯OC¯.

 PROOF Statements Reasons 1. ABCD is a kite with AC and BD asdiagonals that intersect at ‘O’ 1. Given 2. AB≅BCAD≅CD 2. Two pairs of the adjacent sides of a kiteare congruent 3. BD¯≅BD¯ 3. Identity. 4. ∆ABD≅∆BCD 4

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