Draw a quadrilateral and mark the midpoints of each side, join these midpoints to form another quadrilateral. What is the appropriate name for this quadrilateral?
[Rectangle, Square, Trapezium, Parallelogram]
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Given : a quadrilateral
midpoints of each side joined to form another quadrilateral.
To Find : appropriate name for this quadrilateral
Solution:
line joining the mid-point of two sides of a triangle is equal to half the length of the third side
Let say Quadrilateral is ABCD
and mid points are P Q R S are mid point fo AB , BC , CD and AD respectively
in ΔABC
PQ = AC/2
in ΔADC
RS = AC/2
=> PQ = RS
Similarly
QR = PS = BD/2
Hence pair of opposite sides are equal
so its a parallogram
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