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

thkite7given
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.
∠BEA congruent ∠BEC.
7.
CPCTC-corres partscongruentΔs arecongruent
8.
∠BEA supp ∠BEC
8.
Angles forming a linear pair are supplementary.
9.
m∠BEA + m∠BEC = 180
9.
Supplementary ∠s are 2 ∠s whose measures add to 180º.
10.
m∠BEA = m∠BEC
10.
congruent∠s are ∠s of = measure.
11.
m∠BEA + m∠BEA = 180
11.
Substitution
12.
2m∠BEA = 180
12.
Add (or combine like terms).
13.
m∠BEA = 90
13.
Division
14.
∠BEA right ∠
14.
A rt. ∠ has a measure of 90º.
15.
thkite715
15.
Perpendicular lines meet to form right angles.

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