Question

what information would you need to prove the triangles below are congruent using the hl theorem? ∠o = 90°, ∠p ≅ ∠n, ∠o ≅ ∠r, ∠o = 90°, om ≅ rq, ∠o ≅ ∠r, ∠p ≅ ∠n, ∠o ≅ ∠r

Explanation:

Step1: Recall HL - Hypotenuse - Leg theorem

The HL theorem states that if the hypotenuse and one leg of a right - triangle are congruent to the hypotenuse and one leg of another right - triangle, then the two right - triangles are congruent.

Step2: Identify right - angles

We need to know that the triangles are right - triangles. So we need to have $\angle O = 90^{\circ}$ and $\angle P=90^{\circ}$

Step3: Identify congruent hypotenuse and leg

We also need to know that one leg and the hypotenuse are congruent. For example, $OM\cong RQ$ and $ON\cong RP$ (but this is not among the options). The key for the HL theorem is the right - angle information.

Answer:

$\angle O = 90^{\circ}$ and $\angle P = 90^{\circ}$