Question

Based only on the given information is it Guaranteed that angle ABD is congruent to Angle CBD

Answer 1

Yes, it is guaranteed that the triangles are congruent.

Answer = True

Answer 2

The information is true for ∠ABD ≅ ∠CBD .

Reason

In the Δ ABD and ΔCBD

BD = BD

(Common sides of both the triangles)

∠A = ∠C = 90 °

AD = CD

(As shown in the disgram)

now by using SAS Congurence property.

Δ ABD ≅ ΔCBD

Thus ∠ABD ≅ ∠CBD

(By corresponding sides of the congurent triangles.)

Therefore

its true that ∠ABD is congruent to ∠ CBD .