Question

a side - side - side congruent triangle theorem
b side - angle - side congruent triangle theorem
c angle - angle - side congruent triangle theorem
d
e hypotenuse leg congruent triangle theorem

Explanation:

Step1: Analyze the given information

We have a triangle with a side - angle - side configuration. One side is marked as equal (the side between the given angle and another side), an angle is marked, and another side is marked (the side adjacent to the given angle).

Step2: Recall the congruent triangle theorems

• Side - Side - Side (SSS): Requires three sides to be equal.
• Side - Angle - Side (SAS): Requires two sides and the included angle to be equal.
• Angle - Angle - Side (AAS): Requires two angles and a non - included side to be equal.
• Hypotenuse Leg (HL): For right - angled triangles, requires hypotenuse and a leg to be equal.

Since we have two sides and the included angle (the angle between the two marked sides), the Side - Angle - Side Congruent Triangle Theorem applies.

Answer:

B. Side - Angle - Side Congruent Triangle Theorem