Question

given the triangles below with sides and angles as marked.
select the postulate or theorem that proves these triangles are congruent.
side angle side congruence postulate
side side side congruence postulate
hypotenuse leg congruence theorem
angle angle side congruence theorem
angle side angle congruence postulate
these triangles are not congruent

Explanation:

Step1: Recall congruence criteria

The Angle - Angle - Side (AAS) congruence theorem 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.

Step2: Analyze the given triangles

In the two triangles, we have two pairs of congruent angles (marked with the same number of arcs). Also, the side (though not shown as a marked side - but in the context of triangle congruence, when two angles are known, the third angle is also known due to the angle - sum property of triangles (\(A + B + C=180^{\circ}\)). And the non - included side (the side that is not between the two marked angles) can be considered for the AAS criterion. Since we have two angles congruent in each triangle (by the angle markings) and the non - included side (by the nature of triangle congruence when two angles are fixed, the side opposite one of the non - common angles can be used for AAS), the Angle Angle Side Congruence Theorem applies.

Answer:

Angle Angle Side Congruence Theorem