Pythagoras Theorem and Its Converse from "summary" of NCERT Class 10 Mathematics Solutions by JagranJosh
Pythagoras Theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In simpler terms, if we have a right-angled triangle with sides a, b, and c (where c is the hypotenuse), then a² + b² = c². This theorem is widely used in geometry to find the length of a side in a right-angled triangle if the other two sides are known. The converse of Pythagoras Theorem is also true, which means that if the square of the longest side in a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right-angled triangle. In other words, if a² + b² = c², then the triangle with sides a, b, and c is a right-angled triangle. This converse theorem helps in determining whether a given triangle is a right-angled triangle or not. To prove the converse of Pythagoras Theorem, we start by assuming that a triangle with sides a, b, and c satisfies a² + b² = c². We then proceed to show that the triangle is a right-angled triangle. This can be done by constructing perpendiculars from the vertices of the triangle to the sides and using the properties of similar triangles to establish that the angles of the triangle are 90 degrees. The converse of Pythagoras Theorem is a useful tool in geometry as it helps in identifying right-angled triangles based on the lengths of their sides. It is essential to understand both Pythagoras Theorem and its converse to solve problems related to right-angled triangles effectively. By applying these theorems, we can determine unknown side lengths, angles, and other properties of right-angled triangles with ease.
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