Question

This question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:

(a) Both Assertion (A) and Reason (R) are true and Reason (R) correct explanation of Assertion (A).

(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

(c) Assertion (A) is true and Reason (R) is false.

(d) Assertion (A) is false and Reason (R) is true.

Answer 1

ANSWER:
(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
Given: A trapezium $ABCD$, $AB\parallel DC$.

When two triangles are on the same base and between the same parallel lines then the area of two triangles is equal.

Since, $\Delta ADB$ and $\Delta ABC$ are on the same base $AB$ and between the same parallel lines $AB$ and $DC$.

Hence, $ar\left(\Delta ADB\right)=ar\left(\Delta ABC\right)$.

Now subtracting common area of the triangle $\Delta AOB$ from both the sides, we get,

$\Rightarrow ar\left(\Delta ADB\right)-ar\left(\Delta AOB\right)=ar\left(\Delta ABC\right)-ar\left(\Delta AOB\right)$

$\Rightarrow ar\left(\Delta AOD\right)=ar\left(\Delta BOC\right)$

Hence, proved.