50 points! name the postulate or theorem .

 
Choice B) HL Theorem



Explanation:

NP is perpendicular to OM. The upside-down T shape means "perpendicular". So we have the two right angles NHM and OHP which are both 90 degrees (so they are congruent to one another). This further means triangle NHM and triangle OHP are right triangles. 

Because they are right triangles, this means we can use the special right triangle congruence properties. Specifically we can use the HL Theorem. HL stands for "Hypotenuse Leg". We're given NM = OP, which are the two corresponding hypotenuses. Since HMP is isosceles with base MP, this means HM = HP which are the corresponding congruent legs. We have a pair of hypotenuses and a pair of legs congruent; therefore, the triangles are congruent by the HL Theorem.

9.8? i'm not really sure