Question

the hl congruence theorem quick check 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 can conclude that they are congruent because they are both right triangles. he could use the given side lengths and apply the concept of hl. he could apply hl congruence theorem because the hypotenuses are congruent and each have a right angle. he could apply the pythagorean theorem to find the missing side lengths and then compare corresponding sides to apply hl.

Explanation:

The HL (Hypotenuse - Leg) Congruence Theorem states that if the hypotenuse and a leg of one right - triangle are congruent to the hypotenuse and a leg of another right - triangle, the two right - triangles are congruent. Here, we know the hypotenuse of both right - triangles is 13 units. For the first triangle with a leg of 12 units, using the Pythagorean Theorem \(a^{2}+b^{2}=c^{2}\) (where \(c = 13\) and \(a = 12\)), we can find the other leg \(b=\sqrt{13^{2}-12^{2}}=\sqrt{169 - 144}=\sqrt{25}=5\) units. For the second triangle with a leg of 5 units, we can find the other leg in the same way and get 12 units. So, we need to find the missing side lengths using the Pythagorean Theorem and then compare corresponding sides to apply HL.

Answer:

He could apply the Pythagorean Theorem to find the missing side lengths and then compare corresponding sides to apply HL.