Question

ABCD b a trapezion in which AB II DC and ito diagenel in feracet each other at the point O. Show that AO = CO​

Answer 1

Answer:

Given parameters

ABCD is a trapezium where AB || DC and diagonals AC and BD intersect at O.

To prove

AOBO=CODO

Construction

Draw a line EF passing through O and also parallel to AB

Now, AB ll CD

By construction EF ll AB

∴ EF ll CD

Consider the ΔADC,

Where EO ll AB

According to the basic proportionality theorem

AEED=AOOC ………………………………(1)

Now consider Δ ABD

where EO ll AB

According to the basic proportionality theorem

DE/EA = DO/BO…………….(ii)

From equation (i) and (ii), we get,

AO/CO = BO/DO

⇒AO/BO = CO/DO

Hence, proved.

Hence the proof..