A kite is a quadrilateral with two pairs of adjacent, congruent sides. Prove the two angles between the non-congruent sides are congruent. Be sure to create and name the appropriate geometric figures. This figure does not need to be submitted.

Question

aihberkhan · Answer

Okay. 

In the kite shown, AD = AB   and  CB = CD (both given).
For proving angle D = angle B, Join D and B.
Triangle ADB is isosceles because AD = AB
Therefore, angle ADB = angle ABD

Do the same analysis for the bottom triangle.

Then add the angles and you can prove angle D = angle B.

To come up with a proof sometimes we have to introduce a construction.
Here I joined the opposite vertices B and D so that I can split the kite into two isosceles triangle.  That helps us in proving angle B = angle D.

aihberkhan · Answer

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nicoleg7 · Answer

thank u:-)