Q. 5

# Show that the lin

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

Is parallel and half of 3rd side

Solution:-

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

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

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