Mathematics
In the adjoining figure, AB || DC and AB ≠ DC. If the diagonals AC and BD of the trapezium ABCD intersect at O, then which of the following statements is not true ?
area of △ABC = area of △ABD
area of △ACD = area of △BCD
area of △OAB = area of △OCD
area of △OAD = area of △OBC
Theorems on Area
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Answer
We know that,
Triangles on the same base and between same parallel lines are equal in area.
Hence,
⇒ area of △ABC = area of △ABD …….. (1)
⇒ area of △ACD = area of △BCD
From figure and eqn. (1),
area of (△AOB + △OAD) = area of (△AOB + △OBC)
⇒ area of △OAD = area of △OBC.
Hence, Option 3 is the correct option.
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