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 figure

In the figure, we have two triangles \( \triangle JKM\) and \( \triangle LMK\). We are given two pairs of angles (as indicated by the arc markings) and a non - included side (the common side \(MK\)).

Step2: Recall congruent triangle theorems

• SSS (Side - Side - Side): Requires three pairs of equal sides.
• SAS (Side - Angle - Side): Requires two sides and the included angle.
• AAS (Angle - Angle - Side): Requires two angles and a non - included side.
• ASA (Angle - Side - Angle): Requires two angles and the included side.
• HL (Hypotenuse Leg): For right - angled triangles.

Since we have two angles and a non - included side, the AAS (Angle - Angle - Side) congruent triangle theorem applies.

Answer:

C. Angle - Angle - Side Congruent Triangle Theorem