Question

1. choose the correct answer.

which theorem or postulate could be used to prove the congruence of the triangles?
aas
asa
sas
ssa

Explanation:

• AAS (Angle - Angle - Side):
• In the given figure, we have two pairs of congruent angles (the marked angles in the triangles) and a pair of congruent non - included sides (the sides that are marked as equal).
• The AAS congruence criterion 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.
• ASA (Angle - Side - Angle):
• For ASA, the side should be included between the two angles. In the given figure, the equal side is not included between the two marked angles, so ASA does not apply.
• SAS (Side - Angle - Side):
• For SAS, we need two sides and the included angle. Here, we have two angles and a side, not two sides and an included angle, so SAS is not applicable.
• SSA (Side - Side - Angle):
• SSA is not a valid congruence criterion in general (except for the right - triangle case where it is equivalent to HL). Since we are not dealing with right - triangles here and SSA does not guarantee congruence for all triangles, it cannot be used.

Answer:

A. AAS