Proof for Theorem
Prove: If a quadrilateral is a kite, it has one pair of opposite angles congruent.

pfkitegiven
thkite1
 
Statements
  
Reasons
1.
kite ABCD
1.
Given
2.
Draw bd
2.
Two points determine exactly one line.
3.
phkite3
3.
A kite has 2 distinct sets of congruent adjacent sides.
4.
bdcongruent bd
4.
Reflexive property.
5.
pfkite5
5.
SSS - if 3 sides of 1 Δ are congruent to the corres. parts of other Δ, the Δs are congruent.
6.
∠A congruent ∠C
6.
CPCTC-corres partscongruentΔs arecongruent
7.
Assume ∠B congruent ∠D.
7.
Assumption leading to a contradiction.
8.
ABCD is parallelogram
8.
If a quadrilateral has 2 sets of opp. ∠scongruent, it's a parallelogram.
9.
pfkite19
9.
Contradiction steps 9 and 1.
(A kite is not a parallelogram.)

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