Let ABCD be a parallelogram. We have that M is the midpoint of AB and N is the midpoint of BC. The segments DM and DN intersect AC at P and Q, respectively. If AC = 15 and DN = 35, what is DQ?
+130071 See the image below
Because AB and DC are parallels cut by transversal AC, then angles DAQ and NCQ are equal alternate interior angles
And angle PQD = angle CQN (vertical angles)
So...by AA congruency , triangle AQD is similar to triangle CQN
But NC = (1/2) of BC so it also equals (1/2) of AD
Then NC : AD = 1 : 2
But this also means that QN : QD = 1 : 2
So QD = [ 2 / ( 1 + 2) ] DN = (2/3) (35) = 70 / 3
