Question

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

Explanation:

Step1: Analyze the given information

We have two triangles with sides marked as equal. The two triangles share a common vertical angle (which are equal as vertical angles are congruent).

Step2: 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.
• Hypotenuse - Leg (HL): Applies only to right - angled triangles.
• Side - Angle - Side (SAS): Two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.
• Angle - Side - Angle (ASA): Two angles and the included side of one triangle are equal to two angles and the included side of another triangle.
• Angle - Angle - Side (AAS): Two angles and a non - included side of one triangle are equal to two angles and the corresponding non - included side of another triangle.

In our case, we have two sides equal (marked) and the included angle (vertical angles) equal.

Answer:

Side Angle Side Congruence Postulate