Theorem 8.6 The diagonals of a parallelogram bisect each other Given : ABCD is a Parallelogram with AC and BD diagonals & O is the point of intersection of AC and BD To Prove : OA = OC & OB = OD Proof : Since, opposite sides of Parallelogram are parallel. The Equation 2 gives. Verify your number to create your account, Sign up with different email address/mobile number, NEWSLETTER : Get latest updates in your inbox, Need assistance? Hence diagonals of a parallelogram bisect each other [Proved]. Thus the two diagonals meet at their midpoints. This is exactly what we did in the general case, and it's the simplest way to show that two line segments are equal. Thus the two diagonals meet at their midpoints. google_ad_client = "pub-9360736568487010"; . In AOD and BOC OAD = OCB AD = CB ODA = OBC AOD BOC So, OA = OC & OB = OD Hence Proved. Prove that the diagonals of a parallelogram bisect each other. That is, each diagonal cuts the other into two equal parts. Then the two diagonals are c = a + b (Eq 1) d = b - a (Eq 2) Now, they intersect at point 'Q'. We show that these two midpoints are equal. Start studying Geometry. In a quadrangle, the line connecting two opposite corners is called a diagonal. The position vectors of the midpoints of the diagonals AC and BD are ` (bar"a" + bar"c")/2` and ` (bar"b" + bar"d")/2`. If possible I would just like a push in the right direction. The angles of a quadrilateral are in the ratio 3: 5: 9: 13. In this video, we learn that the diagonals of a parallelogram bisect each other. To prove that AC and BD bisect each other, you have to prove that AE = EC = BE = ED. In any parallelogram, the diagonals (lines linking opposite corners) bisect each other. Google Classroom Facebook Twitter Angles EDC and EAB are equal in measure for the same reason. 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