Question

ABCD is a trapezium and M,N are midpoints of the diagonal
AC and BD. Then MN is equal to

Answer 1

Answer:

ABCD is a trapezium in which AB || CD and M and N are mid-points of diagonal AC and BD respectively.

Construction: Join AN and produce it to meet CD at E.

To prove: MN = (CD-AB) and MN || CD

Proof: In AANB and AEND

ZANB = ZEND (vertically opposite angles)

NB = ND (N is the mid-points of BD)

and ZABN=ZEDN (alternate angles)

(AB || CD and BD is a transversal)

ΔΑΝΒ = ΔΕΝD (by ASA congruency rule)

⇒ AN = NE and AB = ED ...(i) (by

c.p.c.t)

[17/10, 10:12 pm] ~Now in AEAC,

N and M are the mid-points of AE and AC respectively.

MN || EC and MN = // EC (by mid point theorem)

⇒ MN || EC

and MN = (CD-ED) = (CD-AB)

[using (i)]

Hence, MN || CD (*.* MN || EC) and MN = (CD-AB).

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