Answer :


Given:- ABCD is a quadrilateral


Formula used:- Line joining midpoints of 2 sides of triangle


Is parallel and half of 3rd side


Solution:-


BD is diagonal of quadrilateral


EH is the line joined by midpoints of triangle ABD,


EH is parallel and half of BD


GF is line joined by midpoints of side BC&BD of triangle BCD


GF is parallel and half BD


If HE is parallel to BD and BD is parallel to GF


It gives HE is parallel to GF


If HE is half of BD and GF is also half of BD


It gives HE is equal to GF


AC is another diagonal of quadrilateral


GH is the line joined by midpoints of triangle ADC,


GH is parallel to AC


GH is half of AC


FE is line joined by midpoints of side BC&AB of triangle ABC


FE is parallel to AC


FE is half of AC


If GH is parallel to AC and AC is parallel to FE


It gives GH is parallel to FE


If GH is half of AC and FE is also half of AC


It gives GH is equal to FE


If both opposite sides are parallel and equal


Then, the quadrilateral is parallelogram


If EFGH is parallelogram


Then their diagonal bisect each other


If diagonal of parallelogram is the line joining midpoint of opposite sides of quadrilateral


Then;


Line joining midpoints of opposite sides of quadrilateral bisect each other.


Conclusion:-


Lines joining midpoints of opposite sides of quadrilateral bisect each other


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