To determine whether the two triangles are congruent, Malik can use the Hypotenuse-Leg (HL) theorem for right triangles. According to the HL theorem, if two right triangles have congruent hypotenuses and one pair of corresponding legs that are congruent, then the triangles are congruent.
In this case, both triangles have a hypotenuse of 13 units. The first triangle has one leg measuring 12 units, while the second triangle has one leg measuring 5 units. Malik could apply the Pythagorean theorem to find the other leg of each triangle:
For the first triangle:
- \( a^2 + b^2 = c^2 \)
- \( 12^2 + b^2 = 13^2 \)
- \( 144 + b^2 = 169 \)
- \( b^2 = 25 \)
- \( b = 5 \)
For the second triangle:
- \( a^2 + b^2 = c^2 \)
- \( 5^2 + b^2 = 13^2 \)
- \( 25 + b^2 = 169 \)
- \( b^2 = 144 \)
- \( b = 12 \)
Now, we see that the first triangle has legs of 12 and 5, while the second triangle has legs of 5 and 12.
Since both triangles have a hypotenuse of 13 units and one pair of corresponding legs that are congruent (5 units), Malik can prove that the two triangles are congruent by HL.
Therefore, the correct response is: He could apply the concept of HL and show that the two triangles are congruent.
1 answer