Question

1. look at the figure. how can you prove the triangles are congruent?

it is not possible to determine if the triangles are congruent.
△abd ≅ △cbd by the sss postulate.
△abd ≅ △cbd by the sas postulate.

Explanation:

Step1: Identify the sides of the triangles

In \(\triangle ABD\) and \(\triangle CBD\), we have \(AB = CB\) (marked with one - cross), \(AD=CD\) (marked with two - crosses), and \(BD = BD\) (common side).

Step2: Apply the congruence postulate

The SSS (Side - Side - Side) postulate states that if three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent. Since \(AB = CB\), \(AD = CD\), and \(BD=BD\), we can use the SSS postulate.

Answer:

\(\triangle ABD\cong\triangle CBD\) by the SSS Postulate.