+0  
 
0
86
1
avatar

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?

 Apr 22, 2022
 #1
avatar+124595 
+1

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

 

 

cool cool cool

 Apr 22, 2022

33 Online Users