Question

Given: and which theorem or postulate can be used to prove δabd ≅ δcdb?

a. aa
b. asa
c. aas
d. ssa

Answer 1

The theorem or postulate that can be used to prove
`\( \triangle ABD \cong \triangle CDB \) is \( \text{ASA} \) (Angle-Side-Angle).`

Step-by-step explanation:

According to the
`\( \text{ASA} \)` postulate, if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

In this case, if angle
`\( \angle A \)` is congruent to angle
`\( \angle C \)`, angle
`\( \angle B \)` is congruent to angle
`\( \angle D \)`, and side
`\( BD \)` is common to both triangles, then we can apply the
`\( \text{ASA} \)` postulate to establish the congruence of
`\( \triangle ABD \)` and
`\( \triangle CDB \).`

This proof relies on the geometric properties of angles and sides within the triangles, demonstrating that they have corresponding parts that are congruent.