Proof for Theorem
Prove: If a quadrilateral is a kite, its diagonals are perpendicular.

thkite6given
thkite7
 
Statements
 
Reasons
1.
kite ABCD
1.
Given
2.
phkite3
2.
A kite has 2 distinct sets of congruent adjacent sides.
3.
bdcongruent bd; becongruentbe
3.
Reflexive property.
4.
pfkite5
4.
SSS - if 3 sides of 1 Δ are congruent to the corres. parts of other Δ, the Δs are congruent.
5.
∠ABD congruent ∠CBD
5.
CPCTC-corres partscongruentΔs arecongruent
6.
thkite76
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.
thkite67
7.
CPCTC-corres partscongruentΔs arecongruent
8.
thkite68
8.
A segment bisector forms two congruent segments.

There is only ONE diagonal that bisects the other.
Diagonal ac does not bisect diagonal bd. Since thkite3addby the definition of a kite, thkite6add
will not be the sides of two congruent triangles.

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