Question

Which triangles are similar? Fast please and show work!

Answer 1

here,

Q is the midpoint of PR.

O is the midpoint of PN.

So, the line joining the midpoints of two sides is half and parallel to the third side.

So, QO is parallel to NR.

Now,

in triangles OPQ and NPR,

i) angle OPQ = angle NPR (common angle)

ii) angle POQ = angle PNR (corresponding angles)

iii) angle OQP = angle NRP (corresponding angles)

so,

triangle OPQ is similar to triangle NPR.

(by AAA similarity)