Question

Id trapezium ABCD (adjoining figure), side AB || side DC, diagonals AC and BD intersect in point O. If AB = 20, DC = 6, OB = 15, then find OD.

Answer 1

side AB || side DC [Given] 

and seg BD is their transversal. 

∴ ∠DBA ≅ ∠BDC [Alternate angles] 

∴ ∠OBA ≅ ∠ODC (i) [D – O – B] 

In ∆OBA and ∆ODC 

∠OBA ≅ ∠ODC [From (i)] 

∠BOA ≅ ∠DOC [Vertically opposite angles] 

∴ ∆OBA ~ ∆ODC [AA test of similarity] 

∴ OB/OD = AB/DC  = [Corresponding sides of similar triangles] 

∴  15/OD = 20/6

 ∴ OD = x = (15 x 6)/20

∴ OD = 4.5 units