9THCBSEMATHS

Areas of Parallelograms and Triangles

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Areas of Parallelograms and Triangles To help you visualize better and prepare comprehensively, here are more practice problems along with explanations to strengthen the concepts. — ### **Problem 1: Prove a Property of a Triangle within a Parallelogram** #### **Problem Statement**: Prove that a triangle formed by joining any vertex of a parallelogram to the … Read more

Step-by-Step Proof of Pythagoras Theorem

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Additional Problems and Applications of Pythagoras Theorem 1. Problem: Length of a Diagonal in a Rectangle A rectangle has a length of 8 cm8 \, \text{cm} and a width of 6 cm6 \, \text{cm}. Find the length of its diagonal. Solution The diagonal divides the rectangle into two right triangles.Using Pythagoras Theorem: d2=l2+w2d^2 = l^2 + w^2 … Read more

Step-by-Step Proof of Pythagoras Theorem

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Statement In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.Mathematically: AC2=AB2+BC2AC^2 = AB^2 + BC^2 Step-by-Step Derivation 1. Construction 2. Algebraic Representation The coordinates of the points are: Using the distance formula to find the hypotenuse ACAC: AC=(b−0)2+(h−0)2AC = \sqrt{(b – 0)^2 … Read more