Akite is a quadrilateral with two pairs of adjacent, congruent sides. prove the two angles between the non-congruent sides are congruent. be sure to create and name the appropriate geometric figures. this figure does not need to be submitted.

∠ABD = ∠ACD

Step-by-step explanation:

Given : ABCD is a quadrilateral

            AB≈AC

            DB≈DC

To Prove : ∠ABD = ∠ACD

Proof : We know that  AB≈AC and  DB≈DC

Draw a line join A and D (refer attached figure)

This divides quadrilateral into two triangles named as ΔABD and ΔACD

Now , We know that

AB≈AC (given) this means AB = AC

DB≈DC(given) this means DB=DC

AD=AD(common)

So , by SSS property of congruency ΔABD and ΔACD are congruent .

( SSS property is when  all three sides in one triangle are the same length as the corresponding sides in the other)

Hence, ΔABD ≅ ΔACD

Since ΔABD ≅ ΔACD (Proved above)

⇒∠ABD = ∠ACD

Thus , Two angles between non-congruent sides are congruent.

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