# Triangles - Concept Points

Class 9 - Mathematics

1. A plane figure bounded by three line segments is called a

**triangle**.2. A triangle can be:

- equilateral (all three sides are equal)

- isosceles (any two sides are equal)

- scalene (all three sides are unequal)

3. A triangle in which one of the angles measures 90° is called a

**right-angled triangle**or simply a right triangle.4. The sum of the angles of a triangle is always

**180°**5. Two figures are congruent, if they are of same shape and same size. Congruent triangles are exactly identical.

7. Congruent triangles have equal areas.

8. If two triangles △ABC and △XYZ are

**congruent under the correspondence**A ↔ X, B ↔ Y and C ↔ Z, then symbolically, △ABC ≌ △XYZ9. The abbreviation ‘

**c.p.c.t.**’ for ‘corresponding parts of congruent triangles.10.

**SAS Congruence Rule**: If two sides and the included angle of one triangle are equal to two sides and the included angle of the other triangle, then the two triangles are congruent.11.

**ASA Congruence Rule**: If two angles and the included side of one triangle are equal to two angles and the side of the other triangle, then the two triangles are congruent.12.

**AAS Congruence Rule**: If two angles and one side of one triangle are equal to two angles and the corresponding side of the other triangle, then the two triangles are congruent.13.

**RHS congruence Rule**: If in two right triangles, hypotenuse and one side of a triangle are equal to the hypotenuse and one side of other triangle, then the two triangles are congruent.14.

**SSS Congruence rule**: If three sides of one triangle are equal to the three sides of anoter triangle, then the two triangles are congruent.15. Angles opposite to equal sides of a triangle are equal. (isosceles triangle)

16. Sides opposite to equal angles of a triangle are equal. (isoceles triangle)

17. Each angle of an equilateral triangle is 60°.

18. Of 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.

19. If two sides of a triangle are unequal, the angle opposite to the longer side is greater

20. In a triangle, side opposite the greater angle is longer.

21. Sum of any two sides of a triangle is greater than the third side.

22. Difference between any two sides of a triangle is less than its third side.

23. In an isosceles triangle, the altitude from the vertex bisects the base.

24. The sum of three altitudes of a triangle is less than the sum of three sides of the triangle.

25. In a right triangle, the hypotenuse is the longest side.

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