Abcd is a trapezium in which ab parallel to dc and its diagonals intersect each other at point o

Calculation: ABCD is a trapezium. Draw OF || BA || CD, intersecting AD in F. FO || AB (from figure) ⇒ DO/OB = DF/FA [basic proportionality theorem] FO || DC (from figure) ⇒ CO/OA = DF/FA [basic proportionality theorem] ⇒ DO/OB = CO/OA So, diagonals of a trapezium divide each other proportionally. ΔAOB and ΔDOC are similar triangle ⇒ A(ΔAOB) : A(ΔDOC) = AB 2 : DC 2 ∴ A(ΔAOB) : A(ΔDOC) = 9 : 4

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Draw a line EF through point O, such that EF || CD In ΔADC, EO || CD By using basic proportionality theorem, we obtain `(AE)/(ED) = (AO)/(OC) ........(1)` In ΔABD, OE || AB So, by using basic proportionality theorem, we obtain `(ED)/(AE) = (OD)/(BO)` `=> (AE)/(ED) = (BO)/(OD) .....(2)` From equations (1) and (2), we obtain `(AO)/(OC) = (BO)/(OD)` `⇒ (AO)/(BO) = (OC)/(OD)` • 3 more Video Tutorials For All Subjects • Similarity of Triangles video tutorial 00:16:50 • Similarity of Triangles video tutorial 00:09:47 • Similarity of Triangles video tutorial 00:27:04 • Similarity of Triangles video tutorial 00:25:01 • Similarity of Triangles video tutorial 00:10:21 • Similarity of Triangles video tutorial 00:11:05 • Similarity of Triangles video tutorial 00:27:15

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