Question

class 10 mathematics chapter 6 all theorem​

Answer 1

• All congruent figures are similar, but it doesn’t mean that all similar figures are congruent.

• Two polygons with the same number of sides are similar if their corresponding angles are equal, and their corresponding sides are in the same ratio.

• Two triangles are similar if their corresponding angles are equal and corresponding sides are in the same ratio.

• Basic Proportionality Theorem - If a line is drawn parallel to one side of a triangle and intersects the other two sides, then the other two sides are divided in the same ratio.

• Converse of Basic Proportionality Theorem - If a line divides any of the two sides of a triangle in the same ratio, then that line is parallel to the third side.

• SAS (side-angle-side) - In two triangles, if the corresponding angles are equal and one pair of corresponding sides are in the same ratio then the two triangles are similar.

• SSS (side-side-side) criterion - In two triangles, if the sides of any one of the triangles are proportional to the sides of the other triangle, then their corresponding angles are equal, and the two triangles are similar.

• The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

• Pythagoras Theorem - In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

• Hypotenuse²= Base² + Perpendicular²

• Converse of Pythagoras theorem - In a triangle, if square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.

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