SOLUTION: I have never worked on Kite proofs before so I am very lost. Our teaCher is having us practice paragraph proofs. Here is the problem: A kite is a quadrilateral with two pairs of a

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Question 995818: I have never worked on Kite proofs before so I am very lost. Our teaCher is having us practice paragraph proofs.
Here is the problem: A kite is a quadrilateral with two pairs of adjacent, congruent sides. Prove the two angles between the noncongruent sides are congruent. Be sure to create and name appropriate geometric figures.
Here is what I have:
We are given a kite ABCD. It is given that their are two pairs of adjacent,congruent sides. We are then told to prove that the two angles between the non congruent sides are congruent.
I am assuming that we have to draw a diagonal then prove congruency of two triangles then use CPCTC to prove congruecy. Am I right? Thanks for reading.
Found 2 solutions by solver91311, ikleyn:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


The trick to this one is to recognize that the diagonals of a kite are perpendicular. With the diagonals constructed, you have 4 right triangles consisting of two pairs of congruent right triangles (you can prove the right triangles congruent by HL). Then the angles you want are the sum of one of the acute angles of one of the right triangles and one of the acute angles of the other right triangle.

John

My calculator said it, I believe it, that settles it

Answer by ikleyn(52798) About Me  (Show Source):
You can put this solution on YOUR website!
.
. . . Am I right?
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You are right.