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Theorem 8.7 - Chapter 8 Class 9 Quadrilaterals
Last updated at Dec. 16, 2024 by Teachoo
Chapter 8 Class 9 Quadrilaterals
Concept wise
- Previous topics
- Definitions
- Opposite sides of parallelogram
- Opposite angles of parallelogram
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Diagonal of parallelogram
- Theorem 8.8
- Mid point theorem
Transcript
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
