Question

Right triangles upper A upper B upper C and upper D upper E upper F are drawn side by side. Triangle upper A upper B upper C is oriented so that it rests on side upper A upper C. The other triangle is oriented so that it rests on side upper E upper F.
What theorem proves ΔABC≅ΔFED
?

Option #1: the SSS Theorem

Option #2: the SAS Theorem

Option #3: the HL Theorem

Option #4: the ASA Theorem

(1 point)
The correct response is Option #
.

Answer 1

To determine which theorem proves that triangles \( \Delta ABC \) and \( \Delta FED \) are congruent, we should note the characteristics of the triangles:

- Both triangles are right triangles (since they are specified to be right triangles).
- The "HL Theorem" (Hypotenuse-Leg Theorem) states that if in two right triangles, the hypotenuse and one leg of one triangle are equal to the hypotenuse and one leg of another triangle, then the triangles are congruent.

Since both triangles \( \Delta ABC \) and \( \Delta FED \) are right triangles, we can use the HL theorem to show they are congruent.

Thus, the correct response is Option #3: the HL Theorem.