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.