Question

Is there enough information to prove that the triangles are congruent?

If yes provide the correct triangle congruence postulate or theorem and a congruent statement

if no justify your answer

Answer 1

Yes, there is (ASA)

Step-by-step explanation:

Here, we have a side common to the two triangles. That makes S

Also, we can see an angle on both triangles, that makes A

Lastly, there is a right angle on both triangle

That makes another A

So we have the ASA to prove the congruence of the two triangles

Answer 2

Explanation:

From the figure attached,

In the given right triangles ΔADB and ΔCDB,

Statements Reasons

1). ∠BAD ≅ ∠BCD 1). Given

2). BD ≅ BD 2). Reflexive property

3). ΔADB ≅ ΔCDB 3). By LA theorem of congruence of right triangles

Therefore, there is sufficient information to prove the ΔADB and ΔCDB congruent.

Leg-angle theorem (L-A) will be used to prove the right triangles congruent.