Ratio of the Areas of Similar Triangles | Class 10 Geometry | Proof and Explanation

Описание: In this lesson, we explore Theorem 6.6: The Ratio of Areas of Similar Triangles from the NCERT Class 10 Maths book. The theorem states that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.📐✨

This important concept is also referred to as the ‘Area Theorem for Similar Triangles’ or ‘Proportional Area Theorem’. In this lesson, I’ll guide you through the step-by-step proof with a clear explanation for each step. 🎓📘

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🎯 Basic Proportionality Theorem: If a line is drawn parallel to one side of a triangle, intersecting the other two sides at distinct points, it divides those sides in the same ratio.
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🎯 AAA Criterion for Similarity of Triangles: If the corresponding angles of two triangles are equal, then their corresponding sides are in the same ratio, and the triangles are similar.
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🎯 Central Angle Theorem: The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.
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🎯 The Ratio of Areas of Similar Triangles: The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
👉   • Ratio of the Areas of Similar Triangles | ...  👈