Question

decide whether enough information is given to prove that △abd and △cdb are congruent using the sas congruence theorem. explain
options:

• yes, two pairs of sides and their included angles are congruent.
• no, there is only one pair of the congruent sides.
• yes, two pairs of sides and a pair of angles not included by the sides are congruent
• no, the congruent angles are not the included angles

Explanation:

Step1: Analyze the given information

We have two triangles \(\triangle ABD\) and \(\triangle CDB\). The sides \(AB = CD\) (marked with one tick) and \(AD=CB\) (marked with one tick). The included angles \(\angle ABD=\angle CDB\) (marked with red arcs).

Step2: Apply the SAS (Side - Angle - Side) Congruence Theorem

The SAS Congruence Theorem states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
In \(\triangle ABD\) and \(\triangle CDB\), we have:

• \(AB = CD\) (side)
• \(\angle ABD=\angle CDB\) (included angle)
• \(BD = DB\) (common side, so \(BD=BD\))

Answer:

yes, Two pairs of sides and their included angles are congruent.