MATHEMATICS ASSIGNMENT CLASS 10    CHAPTER-11 Area related to Plane Figures Math Assignment Class X : Chapter 11 : Area Related to Plane Figures like triangle, quadrilaterals and circle etc. Area of minor sector, major sector, minor segment , major segment, semi-circle, quadrants etc. ****************************************************************

Theorem 6.6 class 10 mathematics, theorem based on the ratio of area of two similar triangles, theorem based on the relationship between ratio of areas and the corresponding sides. Statement :  The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Given :-   \[\Delta ABC\sim \Delta PQR\] To Prove :- \[\frac{Ar(\Delta ABC)}{Ar(\Delta PQR)}=\left ( \frac{AB}{PQ} \right )^{2}=\left ( \frac{BC}{QR} \right )^{2}=\left ( \frac{AC}{PR} \right )^{2}\] Construction :-      \[Draw\: \: AM\perp BC\: \: and\: PN\perp QR\] Proof :-      \[\Delta ABC\sim \Delta PQR\] \[\therefore \: \: \frac{AB}{PQ}=\frac{BC}{QR}=\frac{AC}{PR}......(1)\]   \[and\: \: \angle A=\angle P,\: \angle B=\angle Q\: ,\: \angle C=\angle R\] \[Area\: of\: \Delta ABC=\frac{1}{2}\times BC\times AM\] \[Area\: of\: \Delta PQR=\frac{1}{2}\times QR\times PN\] \[\frac{Ar(\Delta ABC)}{Ar(\Delta PQR)}=\frac{\frac{1}{2}\times BC\times AM}{\frac{1

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