Question

a side - side - side congruent triangle theorem
b side - angle - side congruent triangle theorem
c angle - angle - side congruent triangle theorem
d angle - side - angle congruent triangle theorem
e hypotenuse leg congruent triangle theorem
f not congruent

Explanation:

Step1: Analyze the given information

We have two triangles. In one triangle, we have two sides and the included angle is not given. In the other triangle, we have two sides and the included angle is not given in a way that matches the first triangle.

Step2: Check congruence theorems

• SSS (Side - Side - Side): Requires all three sides to be equal. We don't have information about all three sides.
• SAS (Side - Angle - Side): Requires two sides and the included angle. The given sides and angles are not in the included - angle configuration.
• AAS (Angle - Angle - Side): Requires two angles and a non - included side. We don't have two angles given.
• ASA (Angle - Side - Angle): Requires two angles and the included side. We don't have two angles given.
• HL (Hypotenuse - Leg): For right - angled triangles. There is no indication of right angles.

Since the given information does not match any of the congruence theorems (SSS, SAS, AAS, ASA, HL), we conclude that the triangles are not congruent.

Answer:

F. Not Congruent