In a trapezium ABCD, AB // DC, E is mid-point of AD and F is mid-point of BC, then : 1. 2EF = 2. 2EF = AB + DC 3. EF = AB + DC 4. EF =

Join AC. Let AC intersects EF at point O. We know that, In trapezium the line joining the mid-points of non-parallel sides are parallel to the parallel sides of trapezium. ∴ AB || EF || DC. 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. By converse of mid-point theorem, The straight line drawn through the mid-point of one side of a triangle parallel to another, bisects the third side. Given, ⇒ EF || DC ⇒ EO || DC In △ ADC, E is mid-point of AD and EO || DC. ∴ O is mid-point of AC. (By converse of mid-point theorem) ∴ EO = (By mid-point theorem) ..........(1) Given, ⇒ EF || AB ⇒ OF || AB In △ ABC, O is mid-point of AC and F is mid-point of BC. ∴ OF = (By mid-point theorem) ..........(2) Adding equations (1) and (2), we get : ⇒ EO + OF = ⇒ EF = ⇒ 2EF = AB + DC. Hence, Option 2 is the correct option.

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In the given figure, l // m // n and D is mid-point of CE. If AE = 12.6 cm, then BD is :
12.6 cm
25.2 cm
6.3 cm
18.9 cm

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The given figure shows a parallelogram ABCD in which E is mid-point of AD and DL // EB. Then, BF is equal to :
AD
BE
AE
AB

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Mathematics

In a trapezium ABCD, AB // DC, E is mid-point of AD and F is mid-point of BC, then : 1. 2EF = 2. 2EF = AB + DC 3. EF = AB + DC 4. EF =

Mid-point Theorem

Related Questions

In the given figure, l // m // n and D is mid-point of CE. If AE = 12.6 cm, then BD is :
12.6 cm
25.2 cm
6.3 cm
18.9 cm

The given figure shows a parallelogram ABCD in which E is mid-point of AD and DL // EB. Then, BF is equal to :
AD
BE
AE
AB

Mathematics

In a trapezium ABCD, AB // DC, E is mid-point of AD and F is mid-point of BC, then : 1. 2EF = 2. 2EF = AB + DC 3. EF = AB + DC 4. EF =

Mid-point Theorem

Related Questions

In the given figure, l // m // n and D is mid-point of CE. If AE = 12.6 cm, then BD is :12.6 cm25.2 cm6.3 cm18.9 cm

The given figure shows a parallelogram ABCD in which E is mid-point of AD and DL // EB. Then, BF is equal to :ADBEAEAB

In the given figure, l // m // n and D is mid-point of CE. If AE = 12.6 cm, then BD is :
12.6 cm
25.2 cm
6.3 cm
18.9 cm

The given figure shows a parallelogram ABCD in which E is mid-point of AD and DL // EB. Then, BF is equal to :
AD
BE
AE
AB