Question

in the figure shown, which theorem can be used to show that △abc ≅ △def? a. the triangles are not congruent. b. sas triangle congruence theorem c. aas triangle congruence theorem d. asa triangle congruence theorem

Explanation:

To determine the congruence theorem for \(\triangle ABC \cong \triangle DEF\), we analyze the given markings:

• Angle \(B\) and angle \(E\) are marked equal (two arcs), angle \(A\) and angle \(D\) are marked equal (one arc), and one side in each triangle is marked equal (the tick mark).
• The AAS (Angle - Angle - Side) Congruence Theorem states that 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, then the triangles are congruent. Here, we have two pairs of congruent angles and one pair of congruent non - included sides, so the AAS Triangle Congruence Theorem applies.
• Option A is incorrect as the triangles are congruent. Option B (SAS) requires two sides and the included angle, which is not the case here. Option D (ASA) requires two angles and the included side, but we have a non - included side with the two angles, so ASA does not apply.

Answer:

C. AAS Triangle Congruence Theorem