Question

1. which of the following criteria always proves triangles congruent? select all that apply.

a. corresponding congruent angle-side-angle
b. corresponding congruent side-angle-side
c. corresponding congruent side-side-angle
d. 3 congruent sides
e. 2 congruent sides
f. 3 congruent angles

Explanation:

Step1: Recall congruence criteria

• 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.
• 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.
• SSS (Side - Side - Side): If three sides of one triangle are congruent to three sides of another triangle, the triangles are congruent.

Step2: Analyze each option

• Option A (ASA): This is a valid congruence criterion.
• Option B (SAS): This is a valid congruence criterion.
• Option C (SSA): This is not a valid congruence criterion (except in the case of right - angled triangles (HL)).
• Option D (SSS): This is a valid congruence criterion.
• Option E (Two congruent sides): Two congruent sides alone do not guarantee triangle congruence.
• Option F (Three congruent angles): Three congruent angles (AAA) only guarantee similarity, not congruence.

Answer:

A. Corresponding congruent Angle - Side - Angle, B. Corresponding congruent Side - Angle - Side, D. 3 congruent sides