Question

1. consider the following triangles.

7a which of these triangles are congruent?

Explanation:

Step1: Recall congruence (ASA) rule

If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent (ASA congruence).

Step2: Analyze triangle A

Triangle A has: included side length $10$ between $99^\circ$ and $46^\circ$.

Step3: Analyze triangle B

Triangle B has: included side length $10$ between $99^\circ$ and $46^\circ$, matching A's ASA criteria.

Step4: Analyze triangle C

Triangle C has side $10$ adjacent to $99^\circ$, but it is not the included side between $99^\circ$ and $46^\circ$, so it does not match.

Step5: Analyze triangle D

Triangle D has a side length of $13$ (not $10$), so it cannot be congruent to A or B.

Answer:

A. Triangle with 99°, 46°, included side 10, B. Triangle with 99°, 46°, included side 10