Question

Based on the information given in the diagram which congruence theorems or postulates could be given as reasons why cde ~ opq

Answer 1

Option C, Option D and Option F are correct.

Explanation:

In the given triangles CDE and OPQ, CD = OP, DE = PQ, ∠DCE = ∠POQ = 90° and ∠CED = ∠PQO

We have to tell the congruence theorems or postulates applied in the triangle for congruence.

Since ∠C = ∠O = 90°, ∠E = ∠Q , and DE = PQ

Therefore Option C. AASis correct.

Since DC = OP (Leg of the triangle), DE = PQ (Hypotenuse)

Therefore by theorem of HL in a right angle triangle is applied.

Option F. HL is correct.

Now DE = PO and ∠E =∠Q

So theorem LA (leg and acute angle) will be applied to prove the congruence.

So Option D. LA is correct.