Posted by Chris on .
In rhombus DEFG, if m<DEF=60, and the shorter diagonal DF has a length of 7, find the length of the side of a rhombus.

Math 
Reiny,
In a rhombus, the diagonals rightbisect each other.
I recognize the 306090 triangle in the diagram.
then
x/2 = 3.5/1
x = 7
(sure enough, triangle DEF is equilateral) 
Math 
Chris,
So one side of the rhombus is equal to seven? I'm still confused as to how you got your answer...

Math 
Reiny,
Ok, I will use a different approach this time.
Hope you make a sketch.
Since one angle is 60º, then its opposite angle is also 60º, properties of a parallelogram.
Which means the other angle pair is 120º each, (angle D = angle F = 120)
Now look at your diagram, don't you see two equilateral triangles,
triange DEF and also triangle DGF.
So all sides in those two triangles must be equal,
since DF = 7 , the sides of the rhomubus are 7 each. 
Math 
Chris,
I see it now,because a diagonal divides a parallelogram into two congruent triangles! Thank you!!