Question

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

Explanation:

Step1: Recall congruence postulates

• Side - Side - Side (SSS): If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.
• Side - Angle - Side (SAS): If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.
• Angle - Side - Angle (ASA): If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent.
• Angle - Angle - Side (AAS): If two angles and a non - included side of one triangle are equal to two angles and the corresponding non - included side of another triangle, the triangles are congruent.
• Hypotenuse - Leg (HL): For right - angled triangles, if the hypotenuse and one leg are equal, the triangles are congruent.

Step2: Analyze the given triangles

• Assume the two shaded gray triangles. Let's consider the information about sides and angles.
• If we assume that the two triangles have two sides equal (marked as equal in the figure) and the included angle (the angle between the two sides) equal (since they are part of the same larger triangle, vertical angles or angles formed by parallel lines etc. can make the included angle equal).
• By the Side - Angle - Side (SAS) congruence postulate, if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the two triangles are congruent.

Answer:

Side Angle Side Congruence Postulate