Question

PLEASE HELP

Triangle ABC and triangle DEF are shown on the coordinate plane.

a coordinate plane with triangles ABC and FED at A 0 comma 0, B 4 comma 0, C 1 comma 3, D 5 comma 2, E 8 comma 5, and F 8 comma 1, segment AC measures 3 and 2 tenths units, angle A measures 72 degrees, segment DF measures 3 and 2 tenths units, and angle F measures 72 degrees

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

ΔABC ≅ ΔFDE by HL
ΔABC ≅ ΔFED by SAS
ΔABC ≅ ΔDEF by HL
ΔABC ≅ ΔDEF by SAS

Answer 1

ΔABC ≅ ΔFED by SAS

Step-by-step explanation:

The congruent triangles in this case are ΔABC ≅ ΔFED by SAS, where SAS stands for Side-Angle-Side congruence.

To prove the congruence, we need to show that the corresponding sides and angles of the two triangles are congruent.

1. The given information tells us that segment AC measures 3.2 units and segment DF measures 3.2 units. So, the corresponding sides of ΔABC and ΔFED are congruent.
2. The given information also states that angle A measures 72 degrees and angle F measures 72 degrees. So, the corresponding angles of ΔABC and ΔFED are congruent.
3. Therefore, using the SAS congruence criterion, we can conclude that ΔABC ≅ ΔFED.