Two similar triangles upper C upper D upper E and upper H upper I upper J are drawn side by side.

Question

What additional information is necessary to prove △CDE≅△HIJ
by the HL Congruence Theorem?

(1 point)
Responses

DE¯¯¯¯¯¯¯¯≅IJ¯¯¯¯¯¯
Modifying above upper D upper E with bar congruent to Modifying above upper I upper J with bar

∠E≅∠J
angle upper E congruent to angle upper J

CE¯¯¯¯¯¯¯¯≅HJ¯¯¯¯¯¯¯¯
Modifying above upper C upper E with bar congruent to Modifying above upper H upper J with bar

∠D≅∠I

Answer 1

To prove triangles \( \triangle CDE \) and \( \triangle HIJ \) congruent using the HL (Hypotenuse-Leg) Congruence Theorem, we need to establish that:

1. Both triangles are right triangles.
2. The lengths of the hypotenuses are equal.
3. The lengths of one corresponding leg of each triangle are equal.

Since the HL theorem focuses on right triangles, confirming that the triangles are right triangles is essential.

Among the options given, the most pertinent additional information required can be summarized as follows:

• Correct Option: One of the corresponding legs should be congruent. This implies we need to know that either \( DE \) is congruent to \( IJ \), \( CE \) is congruent to \( HJ \), or there should be an angle equality of the respective right angles.

However, since you need to select one specific response from the options provided, the best match given is:

DE̅̅̅̅̅̅ ≅ IJ̅̅̅̅̅̅

This means that confirming the congruence of the legs (the sides opposite the right angles) is necessary to apply the HL theorem effectively.