Question

1. name the congruence postulate that proves the triangles are congruent:

a
b
c
a. sss
b. sas
c. asa
d. aas

Explanation:

• AAS (Angle - Angle - Side) Congruence Postulate:
• In the given triangles \(\triangle ABD\) and \(\triangle CBD\):
• We have two pairs of congruent angles (\(\angle A=\angle C\) as marked, \(\angle ABD = \angle CBD=90^{\circ}\)).
• And a pair of congruent non - included sides (the side \(BD\) is common to both triangles).
• The AAS postulate states that if two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, then the two triangles are congruent.
• SSS (Side - Side - Side):
• SSS requires all three sides of one triangle to be congruent to the three sides of another triangle. There is no information given about the lengths of all three sides of the two triangles in the problem, so SSS is not applicable.
• SAS (Side - Angle - Side):
• SAS requires two sides and the included angle to be congruent. Here, we do not have information about two sides and the included angle being congruent, so SAS is not applicable.
• ASA (Angle - Side - Angle):
• ASA requires two angles and the included side to be congruent. The side in the given problem is a non - included side for the two given angles, so ASA is not applicable.

Answer:

D. AAS