# Lesson Proof: The diagonals of parallelogram bisect each other

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 This Lesson (Proof: The diagonals of parallelogram bisect each other) was created by by chillaks(0)  : View Source, ShowAbout chillaks: am a freelancer In this lesson we will prove the basic property of parallelogram in which diagonals bisect each other. Theorem If ABCD is a parallelogram, then prove that the diagonals of ABCD bisect each other. Proof Let the two diagonals be AC and BD and O be the intersection point. We have to prove that O is the midpoint of AC and also the midpoint of BD. Hence, and We will prove using congruent triangles concept. Consider two Triangles ABO and COD. 1. ....( Line AC is a transversal of the parallel lines AB and CD, hence alternate angles). 2. ....(Line BD is a transversal of the parallel lines AB and CD, hence alternate angles). 3. ....(Opposite angles when two lines intersect each other area equal) From conditions 1,2 and 3 Triangle ABO is similar to triangle CDO (By Angle -Angle similar property) Since Triangles are similar, Hence ratio of sides are equal from similar triangles property. .........(4) From theorem that Opposite sides of a parallelogram are equal, ..........(5) From equation (4) and (5) Similarly, Hence, We conclude that AO = CO and BO = DO. QED To learn more about Similar and congruent triangles you can refer to wikipedia article. To learn more about parallelogram you can refer to wikipedia This lesson has been accessed 78139 times.