Question

In the given quadrilateral show that AC divides the quadrilateral into two congruent triangles.​

Answer 1

Step-by-step explanation:

$\sf \: Solution:$

$\sf \: Consider \: the \: \triangle \: ABC \: and \: \triangle ADC$

We have,

AB = AD (Given)

BC = DC (Given)

AC = AC (Common side of the two triangles)

Hence,

$\sf\triangle ABC \: \cong \triangle ADC$

(by SSS criterion of congruency of triangles.)

Also, since the two triangles are congruent, we have,

$\sf \angle BAC= \angle DAC \: and \: \angle BCA= \angle DCA .$

We may conclude that, the longer diagonal divides the kite into two congruent triangles, while the shorter diagonal divides the kite into two isosceles triangles. Also, the longer diagonal is the angle bisector of the two angles at its opposite ends.

Answer 2

∠BAC = ∠DAC and ∠BCA = ∠DCA

Refer to the attachment _/I\_