Given: ABCD is a kite, AB < AD

Prove: The diagonals are perpendicular

Triangle ABE = Triangle CBE
ABCD is a kite
Draw BD and AC intersecting at E
Definition
SSS (Side-Side-Side)
CPCTC
Triangle BAD = Triangle BCD
AC is perpendicular to BD
Given
Algebra
SAS (Side-Angle-Side)
<BEA = <BEC
<BAC = <BCA and <DAC = <DCA
<ABD = <CBD
If the angles in a linear pair are equal, then their sides are perpendicular
AB = BC and CD = DA
If two sides of a triangle are equal, the angles opposite them are equal
BE = BE and DE = DE and BD = BD
Two points determine a line
CPCTC