To determine if Malik can prove that the two right triangles are congruent, we first need to examine the given information:
- Both triangles have a hypotenuse of 13 units.
- The first triangle has one leg measuring 12 units.
- The second triangle has one leg measuring 5 units.
To explore the congruence, we can use the Pythagorean Theorem \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse.
For the first triangle:
- One leg \(a = 12\)
- Hypotenuse \(c = 13\)
Using the Pythagorean theorem to find the other leg \(b\): \[ 12^2 + b^2 = 13^2 \] \[ 144 + b^2 = 169 \] \[ b^2 = 169 - 144 \] \[ b^2 = 25 \implies b = 5 \]
For the second triangle:
- One leg \(a = 5\)
- Hypotenuse \(c = 13\)
Using the Pythagorean theorem: \[ 5^2 + b^2 = 13^2 \] \[ 25 + b^2 = 169 \] \[ b^2 = 169 - 25 \] \[ b^2 = 144 \implies b = 12 \]
Now we have both triangles:
- Triangle 1 has legs of \(12\) and \(5\).
- Triangle 2 has legs of \(5\) and \(12\).
Since both triangles have a hypotenuse of \(13\) and legs of \(5\) and \(12\) (in some order), we can conclude that they are congruent by the Hypotenuse-Leg theorem (HL).
Thus, the answer is: He could apply the concept of HL and show that the two triangles are congruent.