Question

In the given figure, PQRS and PXYZ are two parallelograms of equal area. which of the following statements is true?

• A. area $\Delta YSX$ =area $\Delta SXR$
• B. area$\Delta YSR$ =area $\Delta YXR$
• C. SX || YR
• D. All of the above.

Answer 1

The correct option is D All of the above.

(i)PQRS ia a || gm (given)

$\left(ii\right)area\Delta SXR=\frac{1}{2}area\left(||gmPQRS\right)$
(area of a triangle is $\frac{1}{2}$ the area of ||gm on same base and between the same ||'s)

(iii)PXYZ is a ||gm (given)

(iv)area of a triangle is $\frac{1}{2}$ the area of ||gm on the same base and between the same ||'s)
$area\Delta YSX=\frac{1}{2}area\left(||gmPXYZ\right)$

But area of ||gm PQRS = area of ||gm PXYZ (given)

$\therefore area\Delta YSX=area\Delta SXR$

(v)We observe $\Delta YSX$ and $\Delta SXR$ are on the same base SX and their areas are equal

$\therefore SX||YR$

$\therefore area\Delta YSR=area\Delta YXR$

$({\Delta }^{\prime }s$ an the same base and between the same ||'s)