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.