Question

In trapezium ABCD AB|CD and AB=2CD.M N are the midpoints of AC and BD respectively.Let the perimeter of ABCD be a and the perimeter of quadrilateral CDMN be b. Find a-:b.​

Answer 1

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8th

Maths

Understanding Quadrilaterals

Kinds of Quadrilateral

In a trapezium ABCD if E an...

MATHS

In a trapezium ABCD if E and F be the mid point of the diagonals AC and BD respectively, then EF =

A .

21AB

B .

21CD

C .

21(AB+CD)

D .

21(AB−CD)

December 26, 2019Taher Härshita

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ANSWER

ABCD is a trapezium and E,F are mid-points of diagonal AC and BD

AB∥CD                [ one par of opposite side is parallel in trapezium ]

In △CDF and △GBF

⇒  DF=BF                   [ Since, F is mid-point of diagonal BD ]

⇒  ∠DCF=∠BGF   [ DC∥GB and CG is a transversal ]

⇒  ∠CDF=∠GBF    [ DC∥GB and BD is a transversal ]  

∴  △CDF≅△GBF       [ By ASAcongruence rule ]

⇒  CD=GB         [ C.P.C.T ]     ---- ( 1 )

In △CAG, the points E and F are the mid-points of AC and CG respectively.

∴  EF=2