Chapter 4.2, Problem 27E

### 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 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 â€˜Oâ€™.

Prove:

ACÂ¯âŠ¥BDÂ¯

OAÂ¯â‰…OCÂ¯.

 PROOF Statements Reasons 1. ABCD is a kite with AC and BD asdiagonals that intersect at â€˜Oâ€™ 1. Given 2. ABâ‰…BCADâ‰…CD 2. Two pairs of the adjacent sides of a kiteare congruent 3. BDÂ¯â‰…BDÂ¯ 3. Identity. 4. âˆ†ABDâ‰…âˆ†BCD 4

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