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

From the figure, we can observe that in \(\triangle ABD\) and \(\triangle CDB\):

• \(AB = CD\) (given as one pair of equal sides)
• \(AD=CB\) (given as another pair of equal sides)
• \(\angle ABD=\angle CDB\) (the included angle between the two pairs of sides)

Step2: Check the SAS (Side - Angle - Side) congruence theorem

The SAS congruence theorem states that 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, for \(\triangle ABD\) and \(\triangle CDB\), we have two pairs of sides (\(AB = CD\) and \(AD = CB\)) and their included angles (\(\angle ABD=\angle CDB\)) congruent.

Answer:

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