Home
Class 9
MATHS
In parallelogram ABCD, E and F are mid-p...

In parallelogram ABCD, E and F are mid-points of the sides AB and CD respectively. The lines segments AF and BF meet the line segments ED and EC at points G and H respectively. Prove that :
GEHF is a parallelogram.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • MID-POINT THEOREM

    ICSE|Exercise 4 MARKS QUESTION |15 Videos

  • MID-POINT AND ITS CONVERSE(INCLUDING INTERCEPT THEOREM)

    ICSE|Exercise EXERCISE 12(B)|23 Videos

  • PYTHAGORAS THEORAM

    ICSE|Exercise QUESTIONS|9 Videos

Similar Questions

Explore conceptually related problems

In parallelogram ABCD, E and F are mid-points of the sides AB and CD respectively. The lines segments AF and BF meet the line segments ED and EC at points G and H respectively. Prove that : triangle HEB and FHC are congruent.

In a parallelogram ABCD, E and F are the mid-points of sides AB and CD respectively. Show that the line segments AF and EC trisect the diagonal BD.

In a parallelogram ABCD, E and F are the mid-points of sides BC and AD respectively. Show that the line segment BF and ED trisect the diagonal AC.

D, E and F are the mid-points of the sides AB, BC and CA respectively of A ABC. AE meets DF at O. P and Q are the mid-points of OB and OC respectively. Prove that DPOF is a parallelogram.

L and M are the mid-points of sides AB and DC respectively of parallelogram ABCD. Prove that segments DL and BM trisect diagonal AC.

A B C D is a parallelogram, E\ a n d\ F are the mid-points of A B\ a n d\ C D respectively. G H is any line intersecting A D ,\ E F\ a n d\ B C at G ,\ P\ a n d\ H respectively. Prove that G P=P H

D, E and F are the mid-points of the sides BC, CA and AB respectively of triangle ABC. Prove that: BDEF is a parallelogram.

In Figure, A B C D is a parallelogram. E\ a n d\ F are the mid-points of the sides A B\ a n d\ C D respectively. Prove that the line segments A F\ a n d\ C E trisect (divide into three equal parts) the diagonal B D .

In Figure, A B C D is a parallelogram. E and F are the mid-points of the sides A B and C D respectively. Prove that the line segments A F and C E triset (divide into three equal parts) the diagonal B Ddot

In triangle ABC, D and E are mid-points of the sides AB and AC respectively. Through E, a straight line is drawn parallel to AB to meet BC at F. Prove that BDEF is a parallelogram. If AB = 16 cm, AC = 12 cm and BC = 18 cm, find the perimeter of the parallelogram BDEF.