Question

given: AB ≅AC and ∠BAD ≅ ∠CAD. Prove ∠DBC ≅ ∠DCB.

Answer 1

The given information is:

$\begin{gathered} AB\cong AC \\ \angle BAD\cong\angle CAD \end{gathered}$

Now, the next statement is:

$AD\cong AD\text{ }$

Reason: reflexive property

3. Statement:

$\wedge BAD\cong\wedge CAD$

Reason: SAS congruence rule.

4. Statement:

$BD\cong CD$

Reason: CPCTC - Corresponding parts of congruent triangles are congruent.

5. Statement:

$\angle DBC\cong\angle\text{DCB}$

Reason: in a triangle, angles opposite of congruent sides are congruent.