Question

Which statement correctly names the congruent triangles and justifies the reason for congruence? 15 points

ΔABC ≅ ΔFDE by HL

ΔABC ≅ ΔFED by SAS

ΔABC ≅ ΔDEF by HL

ΔABC ≅ ΔDEF by SAS

Answer 1

The correct statement that appropriately names the congruent triangles and its justification for the congruence is: B. ΔABC ≅ ΔFED by SAS.

How to correctly name and justify the reason for congruence?

First, let us state out the available information that is given to us from the image:

m∠A = m∠F = 72 degrees [one pair of congruent angles]

side AC = side DF = 3.2 units [one pair of congruent sides]

side AB = side FE = 4 units [one pair of congruent sides]

This makes angles A and F included angles in both triangles. What this means is that, based on the SAS congruence theorem, triangles ABC and FED are congruent triangles.

Option B. ΔABC ≅ ΔFED by SAS is correct.