Question

A resident welfare society has developed a land having parallelogram shape of side 12 cm each

and pair of opposite sides is parallel. They divided the land into five parts by joining the mid-

points of consecutive sides of given quadrilateral. Here, one part quadrilateral and another four

parts are triangles. In one middle part, they developed gardening and in rest of the part, they

developed classical musical centres. (i) Name the quadrilateral formed in middle.

(ii) What conclusion you will draw through this activity?​

Answer 1

Answer:

parallelogram:

The opposite sides equal, parallel

SR and P Q are equal and parallel

Ina triangle the line Joining 2 mid

points is parallel and half of the 3rd Side.

Answer 2

Given : A quadrilateral is formed joining mid point of a parallelogram

To Find : the quadrilateral formed in middle.

Solution:

ABCD is a a parallelogram

AB = CD and AB || CD

BC = AD  and BC || AD

line joining the mid-point of two sides of a triangle is equal to half the length of the third side and parallel to third side

Hence   two sides are Parallel to  one Diagonal and half of diagonal

PQ = RS = AC/2  & PQ || RS

And Similarly other two sides are  Parallel to  another Diagonal and half of that diagonal

QR = PS = BD/2 and QR || PS

Hence we get two pair of opposite side parallel and Equal

Hence a parallelogram

quadrilateral formed in middle is a parallelogram

Quadrilateral obtained by joining mid point of a parallelogram is always a parallelogram

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