geometry (please explain)

Question

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

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

 ΔABC ≅ ΔEFD by HL 

ΔABC ≅ ΔDEF by HL 

ΔABC ≅ ΔEFD by AAS 

ΔBAC ≅ ΔDEF by AAS

Answer 1

I woluld go with Hypotenuse-Leg. Learn what each of the reasons mean.

Answer 2

You’re being asked to demonstrate two pieces of knowledge with this question.

1) do you understand the naming conventions for congruent triangles?

Since the first triangle is named ABC, a is the right angle, traveling along the short leg to B, then traveling along the hypotenuse to C.

Therefore, when naming the congruent triangle you must follow the same order. Start at the right angle E, travel along the short leg to F then along the hypotenuse to D. Triangle ABC is congruent to triangle EFD.

2) do you understand the congruence theorems?

Hypotenuse-leg (HL) means in a right triangle you can see that one set of corresponding legs are congruent, which we can see as they are both labeled 4.5 units long, and the hypotenuses are congruent, which we can see because we can count how many units (blocks on the graph) long they are.

Therefore, the first answer choice must be correct.