In the quadrilateral given below, AB || DC || EG. If E is mid-point of AD, prove that (i) G is midpoint of BC (ii) 2EG = AB + CD

(i) Given, EG || AB, we can say that ⇒ EF || AB In △DAB, E is midpoint of AD and EF || AB ∴ F is midpoint of BD (By converse of mid-point theorem). EF = AB .......(1) Given, EG || DC we can say that, FG || DC In △BCD, F is midpoint of BD and FG || DC ∴ G is midpoint of BC (By converse of mid-point theorem). Hence, proved that G is midpoint of BC. (ii) In △BCD, F is midpoint of BD and G is midpoint of BC ∴ FG = DC .......(2) Adding eqn. 1 from part (i) and eqn. 2 we get, EF + FG = AB + DC EG = (AB + CD) 2EG = AB + CD. Hence, proved that 2EG = AB + CD.

In the quadrilateral given below, AD = BC, P, Q, R and S are mid-points of AB, BD, CD and AC respectively. Prove that PQRS is a rhombus.

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ABC is an isosceles triangle with AB = AC. D, E and F are mid-points of the sides BC, AB and AC respectively. Prove that line segment AD is perpendicular to EF and is bisected by it.

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In the quadrilateral given below, AB || DC. E and F are mid-points of non-parallel sides AD and BC respectively. Calculate :
(i) EF if AB = 6 cm and DC = 4 cm
(ii) AB if DC = 8 cm and EF = 9 cm.

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Mathematics

In the quadrilateral given below, AB || DC || EG. If E is mid-point of AD, prove that
(i) G is midpoint of BC
(ii) 2EG = AB + CD

Mid-point Theorem

Related Questions

In the quadrilateral given below, AD = BC, P, Q, R and S are mid-points of AB, BD, CD and AC respectively. Prove that PQRS is a rhombus.

ABC is an isosceles triangle with AB = AC. D, E and F are mid-points of the sides BC, AB and AC respectively. Prove that line segment AD is perpendicular to EF and is bisected by it.

In the quadrilateral given below, AB || DC. E and F are mid-points of non-parallel sides AD and BC respectively. Calculate :
(i) EF if AB = 6 cm and DC = 4 cm
(ii) AB if DC = 8 cm and EF = 9 cm.

Mathematics

In the quadrilateral given below, AB || DC || EG. If E is mid-point of AD, prove that(i) G is midpoint of BC(ii) 2EG = AB + CD

Mid-point Theorem

Related Questions

In the quadrilateral given below, AD = BC, P, Q, R and S are mid-points of AB, BD, CD and AC respectively. Prove that PQRS is a rhombus.

ABC is an isosceles triangle with AB = AC. D, E and F are mid-points of the sides BC, AB and AC respectively. Prove that line segment AD is perpendicular to EF and is bisected by it.

In the quadrilateral given below, AB || DC. E and F are mid-points of non-parallel sides AD and BC respectively. Calculate :(i) EF if AB = 6 cm and DC = 4 cm(ii) AB if DC = 8 cm and EF = 9 cm.

In the quadrilateral given below, AB || DC || EG. If E is mid-point of AD, prove that
(i) G is midpoint of BC
(ii) 2EG = AB + CD

In the quadrilateral given below, AB || DC. E and F are mid-points of non-parallel sides AD and BC respectively. Calculate :
(i) EF if AB = 6 cm and DC = 4 cm
(ii) AB if DC = 8 cm and EF = 9 cm.