Mathematics

In the adjoining figure, X and Y are points on the side LN of triangle LMN. Through X, a line is drawn parallel to LM to meet MN at Z. Prove that area of ∆LZY = area of quad. MZYX.

In the adjoining figure, X and Y are points on the side LN of triangle LMN. Through X, a line is drawn parallel to LM to meet MN at Z. Prove that area of ∆LZY = area of quad. MZYX. Theorems on Area, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

Theorems on Area

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Answer

From figure,

∆LZX and ∆MZX are on the same base XZ and between the same parallel lines LM and XZ.

∴ Area of ∆LZX = Area of ∆MZX

Adding area ∆XZY to both sides of the above equation we get,

⇒ area of ∆LZX + area ∆XZY = area ∆MZX + area ∆XZY

From figure,

∆LZX + ∆XZY = ∆LZY and ∆MZX + ∆XZY = MZYX.

∴ Area of ∆LZY = Area of quadrilateral MZYX.

Hence, proved that area of ∆LZY = area of quadrilateral MZYX.

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