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Show that the line segments joining th...

Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other.

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Let `ABCD` is the given quadrilateral.
Please refer to video to see the diagram with their vector representation.
Let `O` is the origin and `E,F,G and H` are the mid points of sides of quadrilateral.
Then,
`vec(OE) = (veca+vecb)/2`
`vec(OF) = (vecb+vecc)/2`
`vec(OG) = (vecc+vecd)/2`
`vec(OH) = (veca+vecd)/2`
...
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RD SHARMA ENGLISH-QUADRILATERALS-All Questions
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  2. A B C D is a rhombus and P ,\ Q ,\ R ,\ S are the mid-points of A B ,\...

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  3. Show that the line segments joining the mid-points of the opposite s...

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  4. Show that the quadrilateral formed by joining the mid-points of the ...

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  5. A B C D is a rhombus and P ,\ Q ,\ R ,\ S are the mid-points of A B ,\...

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  6. The diagonals of a quadrilateral A B C D are perpendicular. Show that ...

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  7. Show that the quadrilateral, formed by joining the mid-points of the s...

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  8. In Figure, A B C D is a parallelogram. E\ a n d\ F are the mid-points ...

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  9. A B C D is a parallelogram. P is a point on A D such that A P=1/3\ A D...

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  10. P is the mid-point of side A B of a parallelogram A B C D . A line t...

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  11. In Figure, A B C D isa trapezium in which side A B is a parallel to si...

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  12. Prove that the line segment joining the mid-points of the diagonals of...

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  13. In /\ A B C ,\ D ,\ E\ a n d\ F are, respectively, the mid-points of...

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  14. In a triangle /a b c ,\ /A=50^0,\ /B=60^0a n d\ /C=70^0 . Find the mea...

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  15. In a triangle, P ,\ Q\ a n d\ R are the mid-points of sides B C ,\ ...

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  16. In a A B C median A D is produced to X such that A D=D X . Prove that...

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  17. In a A B C ,\ E\ a n d\ F are the mid-points of A C\ a n d\ A B respe...

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  18. In a /\ A B C ,\ B M\ a n d\ C N are perpendiculars from B\ a n d\ C...

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  19. In triangle A B C is right-angled at B. Given that A B=9cm ,\ A C=15 ...

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  20. M ,\ N\ a n d\ P are the mid-points of A B ,\ A C\ a n d\ B C respecti...

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