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.
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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