Question

Given:

AB = CD
BC = DA

Prove:
B = D

Which of the following triangle congruence theorems would be used in this proof?

SSS
SAS
ASA

Answer 1

SSS

Explanation:

the triangles would be proven congruent by SSS

AC is equal AC because of the reflexive property (it is equal to itself).

Answer 2

We used SSS rule of congruence to prove that the triangles are congruent.

Explanation:

We are given the following information in the question:

AB = CD

BC = DA

We have to prove that

`\angle B = \angle D`

We will first prove the congruency of triangle.

`\text{In }\triangle ABC \text{ and } \triangle CDA`

AB = CD ( Given )

BC = DA ( Given )

AC = CA (Common )

Hence,
`}\triangle ABC \cong \triangle CDA` by SSS rule of congruence( Side Side Side).

Since the triangles are congruent,
`\angle ABC = \angle CDA`