Question

Which of the following cannot be used to prove
that two triangles are congruent?
A. AAS congruence postulate
B. SAS congruence postulate
C. SSS congruence postulate
D. AAA congruence postulate

Answer 1

Given:

Different types of congruence postulates.

To find:

Which cannot be used to prove  that two triangles are congruent?

Solution:

According to AAS congruence postulate, if two angles and a non including sides of two triangles are congruent, then triangles are congruent.

According to SAS congruence postulate, if two sides and an including angle of two triangles are congruent, then triangles are congruent.

According to SSS congruence postulate, if all three sides of two triangles are congruent, then triangles are congruent.

AAA states that all three angles of two triangles are equal and no information about sides.

So, it is a similarity postulate not congruent postulate. According to AAA two triangles are similar not congruent.

Therefore, the correct option is D.

Answer 2

The AAS, SAS, and SSS congruence postulates can be used to prove that two triangles are congruent. The congruence postulate that cannot be used is: D. AAA congruence postulate

Referring to the image attached below, recall the following:

• Two triangles are congruent by SSS if all three sides of both triangles are congruent to each corresponding sides.
• Two triangles are congruent by SAS if an included angle and two sides in one triangle are congruent to a corresponding included angle and two corresponding sides in the other triangle.
• Two triangles are congruent by ASA if two triangles have an included side and two corresponding angles that are congruent.
• Two triangles are congruent by the AAS if they both have two congruent angles and a corresponding non-included side that are congruent to each other.

Therefore, the AAS, SAS, and SSS congruence postulates can be used to prove that two triangles are congruent. The congruence postulate that cannot be used is: D. AAA congruence postulate

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