Proof For Cross Diagonals Of A Kite

Question

Given: quadrilateral ABCD, BD intersects AC at E, And BD bisects angle ABC and angle ADC

 

Prove: AE=EC

Answer 1

 

The definition of quadrilateral given in the other answer is not 100% accurate.  In many cases, the opposite sides of quadrilaterals are congruent ... ( square, rectangle, parallelogam, rhombus, for example) ... but there are some polygons that do not have 2 pairs of congruent sides ... (Kite, Trapezoid, for example)

Answer 2

Quadrilaterals are polygons that have two pairs of congruent sides opposite to each other. Since AC and BD are diagonals that intersect at point E, and point E is the midpoint of the two diagonals, AC and EC are equal to each other.