Geometry For Enjoyment And Challenge
Geometry For Enjoyment And Challenge
91st Edition
ISBN: 9780866099653
Author: Richard Rhoad, George Milauskas, Robert Whipple
Publisher: McDougal Littell
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Chapter 6, Problem 14CR
Solution

To Prove: HMKJ is a kite

Given information: GH¯HM¯GK¯KM¯ is provided in the question which will help to find the solution.

Proof: GH = HK (given)

Hence, GMH=GMK (angle opposite to equal sides are equal)

And, HM = KM (given)

Hence, HJM=MJK (angle opposite to equal sides are equal)

Here, GMH=GMK

  GMH+HMJ=GMK+HMJ

  HMJ+GMK=180.........(1)

Also, GMK+KMJ=180.........(2)

Equate (1) and (2)

So, GMK+HMJ=GMK+KMJ

  HMJ=KMJ

So that, HJ = JK (sides opposite to equal angles are equal)

Hence, HM = KM and HJ = JK

So that, we can say that HMKJ is a kite or rhombus.

Chapter 6 Solutions

Geometry For Enjoyment And Challenge

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