Proof for Theorem
Prove: If a quadrilateral has one diagonal which is the perpendicular bisector of the other, the quadrilateral is a kite.

kiteprove
thkite7
 
Statements
  
Reasons
1.
kiteprove1
1.
Given
2.
thkite67
2.
A bisector of a segment divides the segment into 2 congruent segments.
3.
∠BEA, ∠BEC, ∠DEA, ∠DEC right angles
3.
A ⊥forms right angles.
4.
∠BEA congruent ∠BEC
∠DEA congruent∠DEC
4.
All right ∠s are congruent.
5.
decongruentde; becongruentbe
5.
Reflexive property.
6.
kiteproof2
6.
SAS - if 2 sides and the included ∠ of 1 Δ are congruent to the corres. parts of other Δ, the Δs are congruent.
7.
phkite3
7.
CPCTC-corres partscongruentΔs arecongruent
8.
kite ABCD
8.
A kite is a quadrialteral with two distinct pairs of adjacent congruent sides.

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