Question

Kite is a quadrilateral with two pairs of adjacent, congruent sides. The vertex angles are those angles in between the pairs of congruent sides. Prove the diagonal connecting these vertex angles is perpendicular to the diagonal connecting the non-vertex angles. Be sure to create and name the appropriate geometric figures.

Answer 1

Quadrilateral ABCD is a kite 
AB is congruent to AD -- definition of a kite 
BC is congruent to DC -- definition of a kite 

draw a line segment AC 
AC is congruent to itself -- identity 
triangle ABC is congruent to triangle ADC -- SSS 
angle ABC is congruent to ADC 
QED

Answer 2

The side AC and BD are perpendicular to each other. And the proof is given below.

What is a quadrilateral?

It is a polygon with four sides. The total interior angle is 360 degrees.

Kite is a quadrilateral with two pairs of adjacent, congruent sides.

The vertex angles are those angles in between the pairs of congruent sides.

Let ABCD is a kite.

Then we have

AB = AD and BC = BD (By definition)

AC and BD are the diagonals of the kite.

AC is common for ΔACB and ΔADC.

Then the ΔABC and ΔADC will be similar.

Then the ∠AOB is equal to ∠AOD.

And ∠AOB and ∠AOD will be linear angles.

Then we have

∠AOB + ∠AOD = 180°

∠AOB + ∠AOB = 180°

           2∠AOB = 180°

             ∠AOB = 90°

Then the side AC and BD are perpendicular to each other.

More about the quadrilateral link is given below.

https://brainly.com/question/13805601

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