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. First, we need to find the missing side lengths of the right - triangles using the Pythagorean Theorem ($a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse and $a$ and $b$ are the legs). For the first triangle with hypotenuse $c = 13$ and leg $a = 12$, we find the other leg $b=\sqrt{13^{2}-12^{2}}=\sqrt{169 - 144}=\sqrt{25}=5$. For the second triangle with hypotenuse $c = 13$ and leg $a = 5$, we find the other leg $b=\sqrt{13^{2}-5^{2}}=\sqrt{169 - 25}=\sqrt{144}=12$. Then we can apply the HL Congruence Theorem.

Answer:

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