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The line drawn through the mid-point of one side of a triangle, parallel to another side, intersects the third side at its mid-point.

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`"Consider that PQ is a line segment drawn from the midpoint of AB and" PQ " " BC`
`"By Basic Proportionality Theorem"`
`(AQ)/(QC)=(AP)/(PB)`
`"Since" AP=PB, therefore (AP)/(PB)=1`
`(AQ)/(QC)=1`
`therefore AQ=QC`
`therefore "Q is the midpoint of AC"`
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Theorem 8.10 : The line drawn through the mid-point of one side of a triangle, parallel to another side bisects the third side.

The line drawn from the midpoint of one side of a triangle parallel to another side bisects the third side.

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Prove that the line joining the mid-points of the two sides of a triangle is parallel to the third side.

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RD SHARMA-QUADRILATERALS-All Questions
  1. Let A B C be an isosceles triangle with A B=A C and let D , E ,F be th...

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  2. ABC is a triangle right angled at C. A line through the mid-point M ...

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  3. The line drawn through the mid-point of one side of a triangle, para...

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  4. In Figure, D ,E and F are, respectively the mid-points of sides B C ,C...

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  5. In DeltaA B C , D, E and F are respectively the mid-points of sides ...

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  6. l, m and n are three parallel lines intersected by transversals p an...

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  7. A B C D is a square E , F , G and H are points on AB , BC , CD and D A...

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  8. A B C D is a rhombus, E A B F is a straight line such that E A=A B=B F...

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  9. A B C D is a parallelogram. A D is a produced to E so that D E=D C and...

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  10. The line segment joining the mid-points of any two sides of a triangle...

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  11. In a quadrilateral ABCD, CO and DO are the bisectors of /C and /D resp...

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  12. The angle of a quadrilateral are respectively 100^@, 98^@, 92^ Find th...

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  13. In a quadrilateral ABCD , the angles A , B , C and D are in the ratio ...

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  14. The sides B A and D C of a quadrilateral A B C D are produced as shown...

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  15. In a quadrilateral A B C D ,A O and B O are the bisectors of /A and /B...

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  16. In Figure, bisectors of /B and /D of quadrilateral A B C D meet C D an...

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  17. The angle of a quadrilateral are respectively 100^@, 98^@, 92^@ Find t...

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  18. In a quadrilateral ABCD , the angles A , B , C and D are in the ratio ...

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  19. In a quadrilateral ABCD ,CO and DO are the bisectors of /C and /D resp...

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  20. The angles of a quadrilateral are in the ratio 3:5:9: 13. Find all the...

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