In the given figure, AD and CE are medians and DF // CE. Prove that : FB = .

Question

KnowledgeBoat · Accepted Answer

By mid-point theorem, The line segment joining the mid-points of any two sides of a triangle is parallel to the third side and is equal to half of it. By converse of mid-point theorem, The straight line drawn through the mid-point of one side of a triangle parallel to another, bisects the third side. Since, AD and CE are medians. ∴ D is the mid-point of BC and E is the mid-point of AB. In △ BEC, DF || CE and D is the mid-point of BC. ∴ F is the mid-point of BE. (By converse of mid-point theorem) ∴ FB = .......(1) Since, E is the mid-point of AB. ∴ BE = .......(2) Substituting value of BE from equation (2) in (1), we get : ∴ FB = . Hence, proved that FB = .

Mathematics

In the given figure, AD and CE are medians and DF // CE. Prove that : FB = .

Mid-point Theorem

Related Questions

In the given figure, M is the mid-point of AB and DE, whereas N is mid-point of BC and DF. Show that : EF = AC.

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 parallelogram ABCD, E is the mid-point of AB and AP is parallel to EC which meets DC at point O and BC produced at P. Prove that :
(i) BP = 2AD
(ii) O is mid-point of AP.

In a trapezium ABCD, sides AB and DC are parallel to each other. E is mid-point of AD and F is mid-point of BC.
Prove that :
AB + DC = 2EF.

Mathematics

In the given figure, AD and CE are medians and DF // CE. Prove that : FB = .

Mid-point Theorem

Related Questions

In the given figure, M is the mid-point of AB and DE, whereas N is mid-point of BC and DF. Show that : EF = AC.

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 parallelogram ABCD, E is the mid-point of AB and AP is parallel to EC which meets DC at point O and BC produced at P. Prove that :(i) BP = 2AD(ii) O is mid-point of AP.

In a trapezium ABCD, sides AB and DC are parallel to each other. E is mid-point of AD and F is mid-point of BC.Prove that :AB + DC = 2EF.

In parallelogram ABCD, E is the mid-point of AB and AP is parallel to EC which meets DC at point O and BC produced at P. Prove that :
(i) BP = 2AD
(ii) O is mid-point of AP.

In a trapezium ABCD, sides AB and DC are parallel to each other. E is mid-point of AD and F is mid-point of BC.
Prove that :
AB + DC = 2EF.