Fig. 9.16Eig. 9.17, PORS andABRS are parallelogramsand X is any point

1.	Fig. 9.16Eig. 9.17, PORS andABRS are parallelogramsand X is any point on side BR. Show that()ar(lPQRS)-ar (ABRS)Q B(ii) ar (ANS)--ar (PORS)
Answer» Parallelograms on the same base and betweenthe same parallels are equal in area. If a parallelogram and a triangle are onthe same base and between the same parallels then area of the triangle is halfthe area of the parallelogram. ========================================================= Given: PQRS & ABRS both are parallelograms and Xis any point on BR. To show: (i) ar (PQRS) = ar (ABRS) (ii) ar (AXS) = ar (PQRS) Proof: (i)Here, Parallelograms PQRS andABRS lie on the same base SR and between the same parallel lines SR and PB. ∴ ar(PQRS) = ar(ABRS) — (i) (ii) In ΔAXS and parallelogram ABRS are lying on the same base AS and betweenthe same parallel lines AS and BR. ∴ ar(ΔAXS)= 1/2 ar(ABRS) — (ii) From eq (i) and (ii), ar(ΔAXS) = 1/2 ar(PQRS) =========================================================

Fig. 9.16Eig. 9.17, PORS andABRS are parallelogramsand X is any point on side BR. Show that()ar(lPQRS)-ar (ABRS)Q B(ii) ar (ANS)--ar (PORS)

Answer»

Parallelograms on the same base and betweenthe same parallels are equal in area.

If a parallelogram and a triangle are onthe same base and between the same parallels then area of the triangle is halfthe area of the parallelogram.

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Given:

PQRS & ABRS both are parallelograms and Xis any point on BR.

To show:

(i) ar (PQRS) = ar (ABRS)

(ii) ar (AXS) = ar (PQRS)

Proof:

(i)Here, Parallelograms PQRS andABRS lie on the same base SR and between the same parallel lines SR and PB.

∴ ar(PQRS) = ar(ABRS) — (i)

(ii) In ΔAXS and parallelogram ABRS are lying on the same base AS and betweenthe same parallel lines AS and BR.

∴ ar(ΔAXS)= 1/2 ar(ABRS) — (ii)

From eq (i) and (ii),

ar(ΔAXS) = 1/2 ar(PQRS)

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