Question

Is there enough information to conclude that the two triangles are congruent? If so, which is the correct congruence statement?

Yes; Triangle CAB is congruent to Triangle DAC
Yes' Triangle ACB is congruent to Triangle ACD
Yes' Triangle ABC is congruent to Triangle ACD
No; the triangles cannot be proven congruent.

Answer 1

Yes' Triangle ACB is congruent to Triangle ACD

Answer 2

Option A. is the correct option.

Explanation:

It is given In the triangle ABC and triangle ADC

Sides AB is congruent to side AD and side AC is common in both the triangles

∠ACD ≅ ∠ACB = 90°

Since triangle ABD is an isosceles triangle, so perpendicular drawn from A to side BD will equally bisect the side BD and ∠ABC ≅ ∠ADC

BC ≅ CD

Therefore, by ASA property in ΔABC and ΔADC

∠ABC ≅ ∠ADC

∠ACB ≅ ∠ACD ≅ 90°

And BC ≅ CD

Therefore, ΔABC ≅ ΔADC

Option A. will the answer.