Properties of Kites: The Angles Between the Unequal Edges are Congruent

It is easy to show that the opposite angles of a kite that are between the two unequal sides are congruent, using congruent triangles.

Problem

ABCD is a kite. Show that ∠ABC≅∠ADC

Strategy

We will show that the two angles are congruent, as corresponding parts of congruent triangles. To do this, we’ll create two triangles in which they are corresponding angles, by drawing the diagonal AC.

Proof

(1) ABCD is a kite    //Given
(2) AB=AD                    //definition of a kite
(3) BC=CD                    //definition of a kite
(4) AC=AC                   //Common side, reflexive property of equality
(5) △ABC≅△ADC   //Side-Side-Side postulate.     
(6) ∠ABC≅∠ADC      //Corresponding angles in congruent triangles (CPCTC)