Question

(a) problem 12: (first taught in lesson 36)
select which shortcut can be used to prove that this pair of triangles are congruent. if no method applies, choose “none.”

Explanation:

Step1: Recall congruence postulates

There are several ways to prove triangle congruence: ASA, SAS, SSS, AAS, HL.

Step2: Analyze ASA

ASA requires two equal angles and the included side to be equal in two triangles.

Step3: Check for given information

We don't have enough information about the markings on the triangles to confirm if ASA applies.

Answer:

We need more information about the markings on the triangles (such as which sides and angles are equal) to determine the congruence - shortcut. Without that information, we cannot give a definite answer. If we assume based on the general congruence - rules:

1. If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent by the Angle - Side - Angle (ASA) postulate.

If the markings on the triangles show two pairs of equal angles and the side between those angles is equal for both triangles, then the answer is A. Angle - Side - Angle. But if the markings do not match this criterion, we need to consider other postulates like Side - Angle - Side (SAS), Side - Side - Side (SSS), Angle - Angle - Side (AAS) or Hypotenuse - Leg (HL) for right - triangles. Since we don't have the full picture of the markings, we cannot be sure.