Final answer:
To determine congruency between two triangles, one must compare their angles and sides through ASA, AAS, or HL congruence rules. If the triangles satisfy the conditions of any of these rules, they are congruent. Step 7 requires checking the answer for consistency with known properties.
Step-by-step explanation:
To determine whether triangles are congruent and by which congruence method (ASA, AAS, or HL), one must compare two triangles for equal angles and sides. The following are congruence rules that help determine triangle congruency:
- Angle-Side-Angle (ASA) Congruence: Two angles and the included side of one triangle are congruent to two angles and the included side of another triangle.
- Angle-Angle-Side (AAS) Congruence: Two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle.
- Hypotenuse-Leg (HL) Congruence (for right triangles only): The hypotenuse and one leg of one right triangle are congruent to the hypotenuse and one leg of another right triangle.
After comparing the given elements of the triangles in question, the correct congruence method can be identified. If the triangles do not satisfy any of these rules, they are not congruent.
Step 7 of the process involves checking whether the answer is reasonable by making comparisons that are consistent with known properties such as the sum of angles in a triangle or the properties of a congruent figures.