Question

1. which of the combinations of sides and angles is sufficient to prove the triangles congruent? choose all that apply:

a. two corresponding sides and the non - included angle.
b. two corresponding angles and the non - included side
c. two corresponding sides and the included angle.
d. two corresponding angles and the included side.

1. identify the vertices of the image under the given transformation. select all that apply:

translation: $(x,y)\to(x + 2,y - 3)$
a. $(-2,-7)$
b. $(5,-10)$
c. $(6,-3)$
d. $(-5,-10)$

Explanation:

Step1: Recall congruence criteria

• AAS (Angle - Angle - Side): If two angles and a non - included side of one triangle are equal to the corresponding two angles and non - included side of another triangle, the triangles are congruent.
• ASA (Angle - Side - Angle): If two angles and the included side of one triangle are equal to the corresponding two angles and included side of another triangle, the triangles are congruent.
• SAS (Side - Angle - Side): If two sides and the included angle of one triangle are equal to the corresponding two sides and included angle of another triangle, the triangles are congruent.
• SSA (Side - Side - Angle): Two sides and a non - included angle do not guarantee triangle congruence.

Step2: Analyze each option

• Option A: Two corresponding sides and the non - included angle (SSA) is not a valid congruence criterion.
• Option B: Two corresponding angles and the non - included side (AAS) is a valid congruence criterion.
• Option C: Two corresponding sides and the included angle (SAS) is a valid congruence criterion.
• Option D: Two corresponding angles and the included side (ASA) is a valid congruence criterion.

Answer:

B. Two corresponding angles and the non - included side, C. Two corresponding sides and the included angle, D. Two corresponding angles and the included side