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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 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 as
diagonals that intersect at ‘O’
1. Given
2. ABBC
ADCD
2. Two pairs of the adjacent sides of a kite
are congruent
3. BD¯BD¯ 3. Identity.
4. ABDBCD 4

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