Question

A kite is a quadrilateral which has 2 sides next to each other that are congruent and where the other 2 sides are also congruent. Given kite WXYZ, shown that at least one of the diagonals of a kite decomposes kite into 2 congruent triangles.

a. Triangle WYX is congruent to Triangle WYZ by AAA.
b. All of the angles are equal.
c. WZ is congruent to WZ and XY is congruent to YZ. WY is congruent to WY since it is in both triangles.
d. The triangles are not congruent at all

Answer 1

To show that at least one of the diagonals of a kite decomposes the kite into 2 congruent triangles, we can use the fact that a kite has two pairs of congruent adjacent sides.

Step-by-step explanation:

To show that at least one of the diagonals of a kite decomposes the kite into 2 congruent triangles, we can use the fact that a kite has two pairs of congruent adjacent sides.

Let's assume that WXYZ is a kite.

By definition, a kite has two pairs of congruent adjacent sides.

Let's assume that XY and WZ are the congruent adjacent sides.

The diagonal WY divides the kite into two triangles, WYX and WYZ. Since XY and WZ are congruent, we can conclude that WYX is congruent to WYZ by the Side-Side-Side (SSS) congruence property.

Therefore, at least one of the diagonals of a kite decomposes the kite into 2 congruent triangles.