Q. 43.9( 10 Votes )

In a parallelogra

Answer :

Given:- ABCD is a parallelogram


E and F are the midpoints of the sides AB and DC respectively


Formula used:- Line drawn through midpoint of one side of triangle


Parallel to other side , bisect the 3rd side.


Solution:-


As ABCD is parallelogram


AB=CD and AB||CD;


AE=CF and AE||CF [E and F are the midpoints of AB and CD]


In quadrilateral AECF


AE=CF and AE||CF


AECF is a parallelogram.


Quadrilateral having one pair of side equal and parallel are parallelogram


If AECF is a parallelogram


AF||CE


Hence ;


PF||CQ and AP||QE [As AF=AP+PF and CE=CQ+QE ]


In Δ DQC


DF=FC [F is midpoint]


PF||CQ


Then;


P is midpoint of DQ


DP=PQ


Line drawn through midpoint of one side of triangle Parallel to


other side , bisect the 3rd side


In Δ APB


AE=EB [E is midpoint]


AP||QE


Then;


Q is midpoint of PB


PQ=QB


Line drawn through midpoint of one side of triangle Parallel to


other side , bisect the 3rd side


If DP=PQ and PQ=QB


Then DP=PQ=QB


Conclusion:-


Line segments AF and EC trisect the diagonal BD.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

ABCD is quadrilatAP- Mathematics

Show that the figAP- Mathematics

In a parallelograAP- Mathematics

ABC is a triangleAP- Mathematics

ABC is a triangleAP- Mathematics

Show that the linAP- Mathematics