The HL Congruence Theorem Quick Check

Question

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Question
Malik is comparing 2 right triangles. Both triangles have a hypotenuse of 13 units. The first triangle has a leg of 12 units and the other triangle has a leg of 5 units. How could Malik prove that the two triangles are congruent?(1 point)
Responses

He could apply the concept of HL and show that the two triangles are congruent.
He could apply the concept of HL and show that the two triangles are congruent.

He could apply the Pythagorean Theorem to show that the two missing sides make both triangles congruent.
He could apply the Pythagorean Theorem to show that the two missing sides make both triangles congruent.

He can conclude that they are congruent because they are both right triangles.
He can conclude that they are congruent because they are both right triangles.

He would need additional information to prove that the two triangles are congruent.
He would need additional information to prove that the two triangles are congruent.
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Answer 1

To determine if the two right triangles Malik is comparing are congruent, we can use the Hypotenuse-Leg (HL) Congruence Theorem. Since both triangles have a hypotenuse of 13 units, we can compare the legs:

• The first triangle has a leg of 12 units.
• The second triangle has a leg of 5 units.

Using the HL theorem, it requires that the hypotenuse is equal and one leg must also be equal. Since we do not have the other leg of the first triangle (which would be needed to prove congruence), and since both legs are not equal (12 ≠ 5), we can conclude that the triangles cannot be congruent based on the given information.

Therefore, the appropriate answer to the question is:

He would need additional information to prove that the two triangles are congruent.