Question

Which of the following statements is true?

a. the triangles are congruent by the SAS congruence postulate

b. the triangles are congruent by the ASA congruence postulate

c. the triangles are congruent by the AAS congruence postulate

d. the triangles are congruent by the SSS congruence postulate

(please explain)

Answer 1

The triangles are congruent by AAS (angle-angle-side).

This becomes clearer when you mark the information it gives you on the diagram, like I've done in the attached image.

If the congruent side was between the two angles, the triangles would be congruent by ASA. Since the graph clearly shows two congruent angles next to each other, and then a congruent side, the answer is AAS.

The ASA (Angle-Side-Angle)

postulate for the congruent triangles: two angles and the included side of one triangle are congruent to two angles and the included side of another triangle; the included side properly represents the side between the vertices of the two angles.

The SAS (Side-Angle-Side)

postulate for the congruent triangles: two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle; the included angle properly represents the angle formed by two sides.

The SSS (Side-Side-Side)

postulate for the congruent triangles: all three sides in one triangle are congruent to the corresponding sides within the other.

The AAS (Angle-Angle-Side)

postulate for the congruent triangles: two pairs of corresponding angles and a pair of opposite sides are equal in both triangles.

Answer 2

The triangles are congruent by AAS (angle-angle-side).
This becomes clearer when you mark the information it gives you on the diagram, like I've done in the attached image.

If the congruent side was between the two angles, the triangles would be congruent by ASA. Since the graph clearly shows two congruent angles next to each other, and then a congruent side, the answer is AAS.

I hope this helps!