In the figure below, the following is true: angleABD congruent to angleCDB and angleDBC congruent to angleBDA. How can you justify that triangleABD congruent to triangleCDB?

Question

Two triangles A B D and C D B are shown with a common segment B D. Segment A B appears to be parallel to D C. A D appears to be parallel to B C.
(1 point)
Responses

SAS
SAS

SSS
SSS

ASA
ASA

CPCTC

Answer 1

To justify that triangle ABD is congruent to triangle CDB, we can use the ASA (Angle-Side-Angle) congruence postulate.

1. We are given that angle ABD is congruent to angle CDB (given: angleABD congruent to angleCDB).
2. We are also given that angle BDA is congruent to angle DBC (given: angleDBC congruent to angleBDA).
3. Segment BD is congruent to itself (reflexive property).

Using the ASA congruence postulate, we have two pairs of congruent angles (angle-angle) and a pair of congruent corresponding sides (side-side). Therefore, triangle ABD is congruent to triangle CDB.