Question

1. determine which theorem can be used to prove triangle congruence.

a. side - side - side
b. side - angle - side
c. angle - side - angle
d. angle - angle - side
e. hypotenuse - leg

1. determine which theorem can be used to prove triangle congruence.

a. side - side - side
b. side - angle - side
c. angle - side - angle
d. angle - angle - side
e. hypotenuse - leg

Explanation:

Step1: Analyze the first pair of triangles

The first pair of triangles has two sides \(12\) and \(16\) and the included right - angle (\(90^{\circ}\)).
By the Side - Angle - Side (SAS) congruence theorem, if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.

Step2: Analyze the second pair of triangles

The second pair of triangles has two angles and a non - included side.
By the Angle - Angle - Side (AAS) congruence theorem, if two angles and a non - included side of one triangle are equal to two angles and the corresponding non - included side of another triangle, the triangles are congruent.

Answer:

For the first pair of triangles: b. Side - Angle - Side.
For the second pair of triangles: d. Angle - Angle - Side.