1. Congruent Figures : Two geometrical figures having exactly the same shape and size known as congruent figures.
2. Congruent Triangles : Two triangles are congruent if and only if one of them can be made to superpose on the other.
3. S – A – S Congruence of Triangle : If two triangles have two side and the included angle of the one equal to the corresponding sides and the included angle of the other then the triangle are congruent.
4. A – S – A Congruence of Triangles : If two angles and the included side of one triangle are equal to the corresponding two angles and the included side of the other triangle then the two triangles are congruent.
5. A – A – S Congruence of Triangles : If two angles and any side of a triangle are equal to the corresponding angles and side of another triangle then the two triangles are congruent.
6. S – S – S Congruence of Triangles : If the three sides of one triangle are equal to the corresponding three sides of another triangle then the two triangles are congruent.
7. R – H – S Congruence of Triangles : Two right – angled triangles are congruent if one side and the hypotenuse of the one are respectively equal to the corresponding side and the hypotenuse of the other.
8. The angles opposite to two equal sides of a triangle are equal.
9. If two angles of a triangle are equal then the side opposite to them are also equal.
10. If two sides of a triangle are unequal then longer side has the greater angle to opposite side.
11. The greater angle has longer side opposite to it.
12. All the line segments that can be drawn to a given line from a point not lying on it, the perpendicular line segment is the shortest.
13. The sum of any two sides of a triangle is greater than third side.
14. The difference between any two sides of a triangle is less than its third side.
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