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)

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

1 answer

Malik could prove that the two triangles are congruent by applying the concept of HL (Hypotenuse-Leg) theorem. Since both triangles have a hypotenuse of 13 units, and one leg of the first triangle is 12 units and the other leg of the second triangle is 5 units, he can check if the missing sides satisfy the triangle properties.

For the first triangle with a hypotenuse of 13 and a leg of 12, he can use the Pythagorean theorem to find the other leg:

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

Assuming the leg is \(b\):

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

This shows that the second leg of the first triangle is also 5 units.

Now, both triangles have:

  • Hypotenuse: 13 units
  • One leg: 12 units (from the first triangle)
  • Other leg: 5 units (from the second triangle)

Since both triangles have two corresponding parts (the hypotenuse and one leg), they can be concluded to be congruent by HL (Hypotenuse-Leg) theorem.

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