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

2. 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.

(Thales’ Theorem).


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


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


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


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


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


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


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

[Pythagoras’ Theorem]


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 Pythagoras’ Theorem]

11. CPCTE represents the condition ‘Corresponding parts of congruent triangles are equal’.

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