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Theorem 8.7 - If diagonals bisect each other, then it is parallelogram

Theorem 8.7 - Chapter 8 Class 9 Quadrilaterals - Part 2
Theorem 8.7 - Chapter 8 Class 9 Quadrilaterals - Part 3

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Theorem 8.7 If the diagonals of a quadrilateral bisect each other, then it is a parallelogram. Given: ABCD is a quadrilateral with AC and BD are diagonals intersecting at O Diagonals bisect each other i.e. OA = OC & OB = OD To Prove: ABCD is a parallelogram Proof : In AOD and COB OA = OC AOD = COB OD = OB AOD COB ODA OBC OAD = OCB Similarly, we can prove AOB COD ABO = CDO Thus, In ABCD, Both pairs of opposite sides are parallel, ABCD is a parallelogram

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.