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.

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. In △ EDF, M is the mid-point of ED and N is the mid-point of DF. ∴ MN = (By mid-point theorem) ⇒ EF = 2MN .............(1) In △ ABC, M is the mid-point of AB and N is the mid-point of BC. ∴ MN = (By mid-point theorem) ⇒ AC = 2MN .............(2) From (1) and (2), we get : ⇒ EF = AC. Hence, proved that EF = AC.

The diagonals of a quadrilateral ABCD are perpendicular to each other. Prove that the quadrilateral obtained by joining the mid-points of its adjacent sides is a rectangle.

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In △ ABC, E is mid-point of the median AD and BE produced meets side AC at point Q. Show that BE : EQ = 3 : 1.

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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.

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Mathematics

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.

Mid-point Theorem

Related Questions

The diagonals of a quadrilateral ABCD are perpendicular to each other. Prove that the quadrilateral obtained by joining the mid-points of its adjacent sides is a rectangle.

In △ ABC, E is mid-point of the median AD and BE produced meets side AC at point Q. Show that BE : EQ = 3 : 1.

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.