Question

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

Explanation:

Step1: Recall congruence postulates

• 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.
• Side - Side - Side (SSS): All three sides of one triangle are equal to all three sides of another triangle.
• 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.
• Hypotenuse - Leg (HL): Applies to right - angled triangles. Hypotenuse and one leg of a right - angled triangle are equal to the hypotenuse and one leg of another right - angled triangle.

Step2: Analyze the given triangles

From the figure (though not fully detailed in text, but based on markings described in general congruence problems of this type), we can assume that we have two sides and the included angle. Let the common side between the two triangles be one side. The two marked equal sides (other than the common side) and the included angle (the angle between the common side and the marked equal sides) satisfy the Side - Angle - Side (SAS) congruence postulate.

Answer:

Side Angle Side Congruence Postulate