Question

Which statement correctly names the congruent triangles and justifies the reason for congruence?

Triangles DEF and ACB on a coordinate plane at D(1, 5), E(2, 7), F(4, 5), A(4, 4), B(4, 1), and C(2, 3). Angle E measures 63 degrees, angle F measures 45 degrees, angle C measures 63 degrees, and angle B measures 45 degrees.
A. ΔBAC ≅ ΔFDE by HL
B. ΔBAC ≅ ΔDEF by HL
C. ΔBAC ≅ ΔFDE by AAS
D. ΔBAC ≅ ΔDEF by AAS

Answer 1

The correct statement is ΔBAC ≅ ΔFDE by AAS. The corresponding angles and included side are congruent.

Step-by-step explanation:

The correct statement is ΔBAC ≅ ΔFDE by AAS.

To justify the congruence, we need to show that two pairs of corresponding angles and the included side are congruent.

1. Angle B and angle E both measure 45 degrees.
2. Angle C and angle F both measure 63 degrees.
3. The side EF is congruent to the side AC.

Therefore, using the Angle-Angle-Side (AAS) congruence criterion, we can conclude that ΔBAC is congruent to ΔFDE.