# Summary

1. Two triangles are said to be similar if (a) their corresponding sides are proportional, and (b) their corresponding angles are equal.Â

2.Â In a triangle, if a line drawn parallel to one of the sides intersects the other two sides in distinct points, then the line divides the two sides in the same ratio.

(Thalesâ€™ Theorem).

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3. If a line divides any two sides of a triangle in the same ratio, then the line will be parallel to theÂ third side.

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4. The bisector of an angle of a triangle, divides the opposites side in the ratio of the sides containing the angle.

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5. If two triangles are equiangular, then the triangles are similar.

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6. If two angles of one triangle are respectively equal to two angles of another triangle, then the triangles are similar.

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7. If the corresponding sides of two triangles are proportional, then they are similar.

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8. If in two triangles, one pair of corresponding sides is proportional and the included angles are equal, then the two triangles are similar.

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9.Â In a right-angled triangle, the square of the hypotenuse in equal to the sum of the squares of the two remaining sides.

[Pythagorasâ€™ Theorem]

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10. If in a triangle the square of one side is equal to the sum of the squares of the other two sides then it will be a right-angled triangle. [Converse of Pythagorasâ€™ Theorem]

11. CPCTE represents the condition â€˜Corresponding parts of congruent triangles are equalâ€™. Â