Question

1. select all of the proofs of triangle congruence * 10 points

□ angle-angle-side (aas)
□ side-angle-side (sas)
□ angle-angle-angle (aaa)
□ side-side-side (sss)
□ angle-side-side (ass)
□ hypotenuse-leg (hl)
□ angle-side-angle (asa)

Explanation:

To determine the valid triangle congruence proofs, we recall the standard congruence criteria:

• AAS (Angle - Angle - Side): If two angles and a non - included side of one triangle are congruent to the corresponding two angles and non - included side of another triangle, the triangles are congruent.
• SAS (Side - Angle - Side): If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the triangles are congruent.
• AAA (Angle - Angle - Angle): AAA only shows similarity, not congruence, as the triangles can have the same shape but different sizes.
• SSS (Side - Side - Side): If three sides of one triangle are congruent to three sides of another triangle, the triangles are congruent.
• ASS (Angle - Side - Side): This is not a valid congruence criterion (it can lead to the ambiguous case in triangles, and does not guarantee congruence).
• HL (Hypotenuse - Leg): This is a special congruence criterion for right - triangles. If the hypotenuse and one leg of a right - triangle are congruent to the hypotenuse and one leg of another right - triangle, the triangles are congruent.
• ASA (Angle - Side - Angle): If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent.

Answer:

A. Angle - Angle - Side (AAS)
B. Side - Angle - Side (SAS)
D. Side - Side - Side (SSS)
F. Hypotenuse - Leg (HL)
G. Angle - Side - Angle (ASA)