Prove that the straight lines joining the mid-points of the opposite sides of a quadrilateral bisect each other.
Mid-point Theorem
2 Likes

Question

Prove that the straight lines joining the mid-points of the opposite sides of a quadrilateral bisect each other.

KnowledgeBoat · Accepted Answer

Let ABCD be the quadrilateral and E, F, G and H be the mid-point of AD, AB, BC and CD. 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. Let ABCD be the quadrilateral and E, F, G and H are the mid-points of sides AD, AB, BC and CD. In △BCD, Since, G and H are the mid-points of BC and CD respectively. ⇒ GH || BD and GH = BD ...(1) In △BAD, Since, F and E are the mid-points of AB and AD respectively. ⇒ FE || BD and FE = BD ...(2) From eq.(1) and (2), we have : ⇒ GH = FE and FE || GH ∴ EFGH is a parallelogram. We know that, Diagonals of the parallelogram, bisect each other. EG and FH are the diagonals of parallelogram EFGH bisects each other. Hence, proved that the straight lines joining the mid-points of the opposite sides of a quadrilateral bisect each other.

Mathematics

Prove that the straight lines joining the mid-points of the opposite sides of a quadrilateral bisect each other.

Mid-point Theorem

Related Questions

In the adjoining figure, ABCD is a trapezium in which AB || DC and E is the mid-point of AD. If EF || AB meets BC at F, show that F is the mid-point of BC.

Two points A and B lie on the same side of a line XY. If AD ⊥ XY and BE ⊥ XY meet XY in D and E respectively and C is the mid-point of AB, show that CD = CE.

BP and CQ are two medians of a △ABC. If QP = 4 cm, then BC =
2 cm
6 cm
8 cm
9 cm

ABC is a right angled isosceles triangle in which ∠A = 90°. If D and E are the mid-points of AB and AC respectively, then ∠ADE =
30°
45°
60°
90°

Mathematics

Prove that the straight lines joining the mid-points of the opposite sides of a quadrilateral bisect each other.

Mid-point Theorem

Related Questions

In the adjoining figure, ABCD is a trapezium in which AB || DC and E is the mid-point of AD. If EF || AB meets BC at F, show that F is the mid-point of BC.

Two points A and B lie on the same side of a line XY. If AD ⊥ XY and BE ⊥ XY meet XY in D and E respectively and C is the mid-point of AB, show that CD = CE.

BP and CQ are two medians of a △ABC. If QP = 4 cm, then BC =2 cm6 cm8 cm9 cm

ABC is a right angled isosceles triangle in which ∠A = 90°. If D and E are the mid-points of AB and AC respectively, then ∠ADE =30°45°60°90°

BP and CQ are two medians of a △ABC. If QP = 4 cm, then BC =
2 cm
6 cm
8 cm
9 cm

ABC is a right angled isosceles triangle in which ∠A = 90°. If D and E are the mid-points of AB and AC respectively, then ∠ADE =
30°
45°
60°
90°