Question

1) In a trapezoid ABCD with legs

AB

and

CD

, the diagonals intersect each other at point O. Compare the areas of: ΔABD and ΔACD


and then


2) In a trapezoid ABCD with legs

AB

and

CD

, the diagonals intersect each other at point O. Compare the areas of:

ΔABO and ΔCDO


pleassssee help

Answer 1

1) Area of ΔABD = Area of ΔACD and

2) Area of ΔABO = Area of ΔCDO

Explanation:

1) In the given trapezoid ABCD,

AD || BC

Triangles ΔABD and ΔACD lie on the same base AD and lie between the parallel lines AD and BC.

Hence, they are equal in area.

Therefore, Area of ΔABD = Area of ΔACD.

2) From 1), we have

Ar (ΔABD) = Ar(ΔACD)

Subtract Ar (ΔAOD) from both sides,

Ar (ΔABD) - Ar (ΔAOD) = Ar(ΔACD) - Ar (ΔAOD)

Ar (ΔABO) = Ar (ΔCDO)