Question

1. what additional information is needed to prove △pmo≅△pno by the hl theorem?

○ (overline{om}congoverline{on})
○ (overline{pm}congoverline{mp})
○ no additional information is needed
○ (angle mopcongangle nop)

Explanation:

Step1: Recall HL - Hypotenuse - Leg theorem

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. In right - triangles $\triangle PMO$ and $\triangle PNO$, $\overline{PO}$ is the common hypotenuse (already congruent to itself).

Step2: Identify the legs

We need to show that one of the legs of the two right - triangles is congruent. The legs are $\overline{OM}$ and $\overline{ON}$. If $\overline{OM}\cong\overline{ON}$, then by the HL theorem, $\triangle PMO\cong\triangle PNO$.

Answer:

$\overline{OM}\cong\overline{ON}$