Question

If the value of q is 16, which of the three triangles can you prove congruent by the HL Congruence Theorem?Three right triangles with vertices and sides labeled.(1 point)Responses△ABC≅△GHI△ABC≅△GHI△EFD≅△GHI△EFD≅△GHI△ABC≅△EFD≅△GHI△ABC≅△EFD≅△GHI△ABC≅△EFD△ABC≅△EFD

Answer 1

To prove triangles congruent using the Hypotenuse-Leg (HL) Congruence Theorem, you need to have two right triangles where you know that:

1. The length of the hypotenuse is equal for both triangles.
2. One leg of each triangle is equal in length.

Assuming you know the values of the sides and the right angle configurations in the triangles you're comparing, you would look for pairs of triangles with these characteristics.

Since you mentioned that the value of \( q \) is 16, that might refer to the length of the hypotenuse or one of the legs of the triangles. Without specific details about the side lengths and triangle configurations, it's difficult to identify specific pairs.

However, the triangles can be grouped into responses as follows:

1. If triangles \( \triangle ABC \) and \( \triangle GHI \) are right triangles and have equal hypotenuses and one equal leg, you can say \( \triangle ABC \cong \triangle GHI \).
2. If triangles \( \triangle EFD \) and \( \triangle GHI \) are also right triangles with equal hypotenuses and one equal leg, you can say \( \triangle EFD \cong \triangle GHI \).
3. If \( \triangle ABC \) and \( \triangle EFD \) both have equal hypotenuses and one equal leg, you can say \( \triangle ABC \cong \triangle EFD \).

Choose the appropriate response based on which pairs of triangles meet the criteria stated above. For example, if triangles are labeled such that \( \triangle ABC \cong \triangle EFD \) because both share the characteristics needed for HL, that would be your answer.

Keep in mind, without exact side lengths or configurations, this is a generalized response based on typical HL criteria.