Question

Q-8.
Line-segment AB is parallel to another line -segment CD. O is the mid-point of AD.
Show that
i) A AOB E ADOC
O is also the mid-point of BC.
С C
D
O
A
B​

Answer 1

Answer:

Given that ABCD is a trapezium with AB || DC and Diagonal AC and BD intersect each other at O.

To prove: Area (AOD) = Area (BOC)

Proof: ΔADC and ΔBDC are on the same base DC and between same parallel AB and DC.

∴Area (ΔADC) = Area (ΔBDC) [triangles on the same base and between same parallel are equal in area]

Subtract Area (ΔDOC) from both side

Area (ΔADC) – Area (ΔDOC) = Area (ΔBDC) – Area (ΔDOC)

Area (ΔAOD) = Area (ΔBOC)