Home
Class 9
MATHS
E is the mid-point of the side AD of the...

E is the mid-point of the side AD of the tarapezium ABCD with `AB||DC`. A line through E drawn parallel to AB intersects BC at F. Show that F is the mid-points of BC.

Text Solution

Verified by Experts

Given ABCD is a trapezium in which `AB||DC and EF||AB||CD`.
Construction Join, the diagonal AC which intersects EF at O.
To show F is the mid-point of BC.

Proof Now, in `Delta`ADC, E is the mid-point of AD and OE`||` CD.
Thus, by mid-point theorem, O is mid-point of AC.
Now, in `Delta`CBA, O is the mid-point of AC and OF `||` AB.
So, by mid-point theorem, F is the mid-point of BC.
Promotional Banner

Topper's Solved these Questions

  • QUADRILATERALS

    NCERT EXEMPLAR ENGLISH|Exercise LONG ANSWER TYPE QUESTIONS|18 Videos

  • QUADRILATERALS

    NCERT EXEMPLAR ENGLISH|Exercise VERY SHORT ANSWER TYPE QUESTIONS|14 Videos

  • POLYNOMIALS

    NCERT EXEMPLAR ENGLISH|Exercise EXERCISE 2.4 Long Answer type Questions|9 Videos

  • STATISTICS AND PROBABILITY

    NCERT EXEMPLAR ENGLISH|Exercise LONG ANSWER TYPE QUESTIONS|12 Videos

Similar Questions

Explore conceptually related problems

In a trapezium ABCD, AB/DC, E is mid-point of aD. A line through E and parallel to AB intersects BC at point F. Show that: 2EF=AB+DC

AB and CD are the parallel sides of a trapeziuml. E is the mid-point of AD. A line through E and parallel to side AB meets the line BC at point F. Prove that F is the mid-point of BC.

ABCD is a trapezium in which A B\ ||\ D C , BD is a diagonal and E is the mid-point of AD. A line is drawn through E parallel to AB intersecting BC at F (see Fig. 8.30). Show that F is the mid-point of BC.

D and F are the mid-points of sides AB and AC of a triangle ABC. A line through F and parallel to AB meets BC at point E. Prove that BDFE is a parallelogram

ABC is a triangle right angled at C and M is mid-point of hypotenuse AB. Line drawn through M and parallel to BC intersects AC at D. Show that: MD is mid-point of AC.

D and F are the mid-points of sides AB and AC of a triangle ABC. A line through F and parallel to AB meets BC at point E. Find AB, if EF=4.8cm .

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.

In the following figure, F and E are points on the side AD of the triangle ABD. Through F a line is drawn parallel to AB to meet BD at point C . Prove that : ar (Delta ACE ) = ar (quad . BCEF )

The diagonals AC and BD of a cyclic quadrilateral ABCD interest at right angles at E (figure). A line l drawn through E and perpendicular to AB meets CD at F. Prove that F is the mid-point of CD.

O is the point of intersection of the diagonals AC and BD of a trapezium ABCD with AB abs() DC. Through O , aline segment PQ is drawn parallel to AB meeting AD in P and BC in Q, prove that PO=QO.