Explain why triangles lmn and nop are similar

work out the length of mo

To prove the two triangles to be similar, it is enough to prove that they have 3 equal angles.
First :
Second :
Third : for the same latter reason, the two angles
Thus we conclude that the 2 triangles MLN and PNO are similar.

Note : if you realized that alternate angles form a letter “ Z “ shape, use this method to easily find them but don’t forget that the alternate angles are equal only when the lines cut by the same third line are parallel.

To find MO : since the two triangles MNL & PNO are similar thus the ratio of the sides facing the angle of common ( equal value ) is equal.
Thus :
ratio of PO/ML = ratio of of PN/NL = ratio of ON/NM

And then we solve :

PO/ML = ON/NM

Substitute the segments by their values :

15/6 = ON/5

Find ON = 12.5 cm

But MO = MN + NO

MO = 5 + 12.5 = 17.5 cm

If you still didn’t understand I can help. Don’t worry ♥️.