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.

Answer 1

To prove that the two right triangles are congruent, Malik could apply the concept of HL (Hypotenuse-Leg) congruence.

In this case, both triangles share the same hypotenuse length of 13 units. The first triangle has one leg of 12 units, while the other triangle has one leg measuring 5 units.

To check if they are congruent by using the HL theorem, he would need to find the length of the missing leg for the first triangle and the missing leg for the second triangle.

Using the Pythagorean theorem:

1. For the first triangle: \[ a^2 + b^2 = c^2 \] \[ 12^2 + b^2 = 13^2 \implies 144 + b^2 = 169 \implies b^2 = 169 - 144 = 25 \implies b = 5 \]

2. For the second triangle, we can assume one leg is 5, and find the other leg (which must match): \[ a^2 + 5^2 = 13^2 \implies a^2 + 25 = 169 \implies a^2 = 169 - 25 = 144 \implies a = 12 \]

Since both triangles have the same hypotenuse and one matching leg (12 in one triangle and 5 in the other), this shows that they indeed satisfy the HL theorem, thus proving that the two triangles are congruent.

So, the best response is: He could apply the concept of HL and show that the two triangles are congruent.