Question

show that the line segment joining the mid points of the opposite sides of a quadrilateral bisect each other​

Answer 1

Step-by-step explanation:

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Answer 2

Let ABCD the quadrilateral and P, Q, R and S are the mid-points of side AB, BC, CD and DA respectively.

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$\large\tt\red{In\:∆ACD,}$

$\small\tt{R\:and\:S\:are\:the\mid-points\:of\:CD\:and\:DA}$

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$\large\tt\green{SR||AC}$.......(1)

$\huge\tt\blue{Similarly,}$

$\large\tt\green{PQ||AC}$.......(2)

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$\huge\tt\purple{From\:(1)\:and\:(2)}$

$\large\tt\green{SR||PQ}$

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$\huge\tt\blue{Similarly,PS||QR}$

$\therefore$$\small\tt\underline\pink{PQRS\:is\:a\:parallelogram}$

$\therefore$$\small\tt\underline\orange{Diagonal\:PR\:and\:SQ\:bisect\:each\:other}$