Question

tion to conclude that the pair of triangles is congruence statement. if not, state any ad- are needed. 32.

Explanation:

Step1: Identify the given information

We have two triangles \( \triangle ABD\) and \( \triangle CBD\). We know that \(AB = CB\) (marked with one - cross), \(AD=CD\) (marked with one - cross), and \(\angle ABD=\angle CBD\) (marked with one - arc).

Step2: Recall the congruence criteria

The congruence criteria for triangles are SSS (Side - Side - Side), SAS (Side - Angle - Side), ASA (Angle - Side - Angle), AAS (Angle - Angle - Side), and HL (Hypotenuse - Leg for right - triangles).

Step3: Check the congruence

We have two sides \(AB = CB\), \(AD = CD\) and the included angle \(\angle ABD=\angle CBD\). So, by the SAS (Side - Angle - Side) congruence criterion.

Answer:

\(\triangle ABD\cong\triangle CBD\) by the SAS congruence statement.