Question

Q.4) Prove that figure obtained by joining the mid points of a quadrilateral is
a parallelogram

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Answer 1

Quadrilateral ABCD is a parallelogram.

Step-by-step explanation:

• given : ABCD is a quadrilateral in which AO=OC ,BO =DO
• TO PROVE : ABCD is a parallelogram.
• PROOF : In Triangle AOD and BOC
• AO=CO (GIVEN)
• BO=DO ( GIVEN)
• AOD=BOC ( VERTICALLY OPPOSITE ANGLE )
• TRIANGLE BOCIS CONGRUENT TO AOB BY SAS .
• ADB = CBD ( CPCT)
• DAC = ACB (CPCT)
• ALTERNATE ANGLES ARE EQUAL
• AD IS PARALLEL TO BC .
• SIMILARLY AB IS PARALLEL TO CD .

IF THE DIAGONALS OF QUADRILATERAL BISECTS EACH OTHER THEN IT IS A PARALLELOGRAM .

THEREFORE,QUADRILATERAL ABCD IS A PARALLELOGRAM .