Question

Fig. 1.59
6. In trapezium ABCD, (Figure 1.60)
side AB || side DC, diagonals AC and
BD intersect in point O. If AB = 20,
DC = 6, OB = 15 then find OD.
95
B
Fig. 1.60​

Answer 1

Answer:side AB is parallel to side DC

And seg BD is their transversal

Therefore,angle DBA is congruent to angle BDC

Therefore,also angle OBA is congruent to angle ODC

In ∆ OBA and ∆ ODC

Angle OBA is congruent to angle ODC

Angle BOA is congruent to angle DOC

Therefore,∆OBA is similar to ∆ODC

OB/OD=AB/DC

15/OD=20/6

Therefore,OD= 15×6/20

Therefore,OD = 4.5 units