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. $\triangle abd=\triangle cdb$ by the sss postulate. $\triangle abd=\triangle cdb$ by the sas postulate.

Explanation:

Step1: Identify the common side

In \(\triangle ABD\) and \(\triangle CDB\), \(BD = BD\) (common side).

Step2: Check the given equal sides and angles

From the figure, \(AD = BC\) (given equal sides), \(\angle ADB=\angle CBD\) (given equal angles).

Step3: Apply the SAS (Side - Angle - Side) Postulate

By the SAS Postulate, if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent. Here, in \(\triangle ABD\) and \(\triangle CDB\), \(AD = BC\), \(\angle ADB=\angle CBD\), \(BD = BD\).

Answer:

\(\triangle ABD\cong\triangle CDB\) by the SAS Postulate.