Akite 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

Let the kite is the quadrilateral A B C D with the two pairs of adjacent congruent sides. (Please find the attached diagram also) 

Now, its given in question, see from figure,

AB is congruent to AD 

BC is congruent to DC 

So, let us join the points A & C to form AC ; and points B and D to form BD. 

So, AC is common side  to triangles ABC and ADC. 

So, Because AB ≈AD

BC ≈ DC

And, AC is common, therefore, 

triangle ABC is congruent to triangle ADC 

⇒∠ ABC ≈ ∠ADC

The above are the angle.