Question

ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O. Show that AO/BO = CO/DO ​

Answer 1

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Answer 2

Answer:-

Accordingly to the given question

ABCD = AB ll CD

AC and BD intersect at point O

AB ll CD and EF ll AB and EF ll CD

ΔADC=EO ll DC

(AE / ED) = (AO / OC) Equation-1

Δ ABD=EO ll AB

Using proportionality Theorem:

(AE / ED) = (BO / OD) Equation-2

From both the equation 1 and 2

(AO / OC) = (BO / OD)

LHS are equal for this

(AO / OC) = (BO / OD)

Proved the answer :-