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?

Question

A. He would need additional information to prove that the two triangles are congruent.
B. He could apply the Pythagorean Theorem to show that the two missing sides make both triangles congruent.
C. He could apply the concept of HL and show that the two triangles are congruent.
D. He can conclude that they are congruent because they are both right triangles.

Answer 1

The correct answer is C. He could apply the concept of HL and show that the two triangles are congruent.

The HL (Hypotenuse-Leg) theorem states that if two right triangles have one leg equal in length and their hypotenuses equal in length, then the triangles are congruent. In this case, both triangles have hypotenuses of 13 units, and one leg of the first triangle is 12 units. To use HL, Malik would need to find the other leg of the first triangle.

Using the Pythagorean theorem for the first triangle:

\( a^2 + b^2 = c^2 \)

Where \( c \) is the hypotenuse (13), and \( a \) is 12. Solving for \( b \):

\( 12^2 + b^2 = 13^2 \)
\( 144 + b^2 = 169 \)
\( b^2 = 169 - 144 \)
\( b^2 = 25 \)
\( b = 5 \)

Now both triangles have a hypotenuse of 13 units and one leg of 5 units, allowing Malik to conclude they are congruent by HL.