In the quadrilateral given below, AB || DC, E and F are mid-points of AD and BD respectively. Prove that (i) G is the mid-point of BC (ii) EG = (AB + DC).

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

In the adjoining figure, ABCD is a parallelogram. E and F are mid-points of the sides AB and CD respectively. The straight lines AF and BF meet the straight lines ED and EC in points G and H respectively. Prove that
(i) △HEB ≅ △HCF
(ii) GEHF is a parallelogram.

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

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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, E and F are mid-points of AD and BD respectively. Prove that (i) G is the mid-point of BC (ii) EG = (AB + DC).

Mid-point Theorem

Related Questions

In the adjoining figure, ABCD is a parallelogram. E and F are mid-points of the sides AB and CD respectively. The straight lines AF and BF meet the straight lines ED and EC in points G and H respectively. Prove that
(i) △HEB ≅ △HCF
(ii) GEHF is a parallelogram.

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 || 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.

Mathematics

In the quadrilateral given below, AB || DC, E and F are mid-points of AD and BD respectively. Prove that (i) G is the mid-point of BC (ii) EG = (AB + DC).

Mid-point Theorem

Related Questions

In the adjoining figure, ABCD is a parallelogram. E and F are mid-points of the sides AB and CD respectively. The straight lines AF and BF meet the straight lines ED and EC in points G and H respectively. Prove that(i) △HEB ≅ △HCF(ii) GEHF is a parallelogram.

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 || 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.

In the adjoining figure, ABCD is a parallelogram. E and F are mid-points of the sides AB and CD respectively. The straight lines AF and BF meet the straight lines ED and EC in points G and H respectively. Prove that
(i) △HEB ≅ △HCF
(ii) GEHF is a parallelogram.

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.