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.

ABCD is a trapezium in which AB || DC and E, F are mid-points of AD and BC respectively. Join CE and produce it to meet BA produced at G. In △EDC and △EAG, ED = EA (∵ E is mid-point of AD) ∠CED = ∠ GEA (Vertically opposite ∠s) ∠ECD = ∠EGA (Alternate ∠s) ∴ △EDC ≅ △EAG ⇒ CD = GA and EC = EG (c.p.c.t.) In △CGB, E is mid-point of CG F is mid-point of BC ∴ By mid-point theorem, EF || AB and EF = GB. But GB = GA + AB = CD + AB ∴ EF = (AB + CD) .....(1) (i) Given, AB = 6 cm and DC = 4 cm, Putting these values in eq (1) we get, EF = (6 + 4) = x 10 = 5 cm Hence, EF = 5 cm. (ii) Given, DC = 8 cm and EF = 9 cm Putting these values in eq (1) we get, 9 = (AB + 8) ⇒ 18 = AB + 8 ⇒ AB = 18 - 8 = 10 cm Hence, AB = 10 cm.

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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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 figure given below, ABCD is a kite in which BC = CD, AB = AD. E, F, G are mid-points of CD, BC and AB respectively. Prove that :
(i) ∠EFG = 90°
(ii) The line drawn through G and parallel to FE bisects DA.

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Mathematics

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.

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.

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 figure given below, ABCD is a kite in which BC = CD, AB = AD. E, F, G are mid-points of CD, BC and AB respectively. Prove that :
(i) ∠EFG = 90°
(ii) The line drawn through G and parallel to FE bisects DA.

Mathematics

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.

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.

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 figure given below, ABCD is a kite in which BC = CD, AB = AD. E, F, G are mid-points of CD, BC and AB respectively. Prove that :(i) ∠EFG = 90°(ii) The line drawn through G and parallel to FE bisects DA.

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 figure given below, ABCD is a kite in which BC = CD, AB = AD. E, F, G are mid-points of CD, BC and AB respectively. Prove that :
(i) ∠EFG = 90°
(ii) The line drawn through G and parallel to FE bisects DA.