Question

Triangle abc and triangle def are shown on the coordinate plane. Triangle abc has coordinates a(0,0), b(4,0), and c(1,3). Triangle def has coordinates d(5,2), e(8,5), and f(8,1). Segment ac measures 3.2 units and angle a measures 72 degrees. Segment df measures 3.2 units and angle f measures 72 degrees. Which statement correctly names the congruent triangles and justifies the reason for congruence?

1) ��abc ��� ��fde by HL
2) ��abc ��� ��fed by SAS
3) ��abc ��� ��def by HL
4) ��abc ��� ��def by SAS

Answer 1

The congruent triangles are Triangle ABC and Triangle DEF, and the reason for congruence is the Side-Angle-Side (SAS) criterion.

Step-by-step explanation:

The congruent triangles in this scenario are Triangle ABC and Triangle DEF. The reason for the congruence is the Side-Angle-Side (SAS) congruence criterion.

To prove the congruence, we can use the following information:

• Segment AC measures 3.2 units, and Segment DF also measures 3.2 units.
• Angle A measures 72 degrees, and Angle F measures 72 degrees.

By SAS, when two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.