Prove: If a quadrilateral is a kite, its diagonals are perpendicular.
Statements
Reasons
1.
kite ABCD
1.
Given
2.
2.
A kite has 2 distinct sets of congruent adjacent sides.
3.
;
3.
Reflexive property.
4.
4.
SSS - if 3 sides of 1 Δ are to the corres. parts of other Δ, the Δs are .
5.
∠ABD ∠CBD
5.
CPCTC-corres partsΔs are
6.
6.
SAS - if 2 sides and the included ∠ of 1 Δ are to the corres. parts of other Δ, the Δs are .
7.
7.
CPCTC-corres partsΔs are
8.
8.
A segment bisector forms two congruent segments.
There is only ONE diagonal that bisects the other.
Diagonal does not bisect diagonal . Since by the definition of a kite,
will not be the sides of two congruent triangles.