Question

AB ABCD is a trapezium in which side ab parallel side DC and its diagonal intersect each other at point O show that AO upon bo is equal to co upon do

Answer 1

Step-by-step explanation:

Given a trapezium ABCD such that AB∥CD.

The diagonals AC and BD meet at O.

We know that,∠A+∠B+∠C+∠D=360°

Since AB∥CD, we have

1. ∠OAB=∠OCD
2. ∠OBA=∠ODC

because alternate interior angles are equal.

⇒ΔOAB∼ΔOCD. Thus in similar triangles ratio of corresponding sides are equal

⇒AOBO=CODO

Hence proved.

Answer 2

in ∆ ADC and ∆ BDC
DC = DC ...... common side
angle ADC = angle BCD ...... property of TREPIZEUM
ad = BC
∆ ADC =~ ∆ BDC ( SAS)
so, ac = bd (c.p.c.t.)