**Triangle** is a closed shape with three sides.

Table of Contents

ToggleTriangles can be classified on the basis of sides and angels.

1. By side

2. By angles

1. Types of triangles by Side

(a) Equilateral Side: all sides are equal

(b) Isosceles triangles

(c) Scalene triangles

(a) Equilateral Side: all sides are equal

(b) Isosceles triangles

(c) Scalene triangles

(ii) Types of triangles by angles.

(i) Acute angled triangle : All angles less than 90^{0}

(ii) Right angled triangles

(iii) Obtuse angled triangle

(i) Acute angled triangle: All angles less than 90^{0}

(ii) Right angled triangles

(iii) Obtuse angled triangle

**Congruence of triangles**

**Congruence: **if two figures or objects are of the same shape and of the same size. They are called as ‘Congruent’. symbolically, we use ‘≅’ for congruence.

- Two circles of the same radii are congruent-
- Two squares of the same sides are congruent.

Rules for congruence of triangles:

(i) SAS = Side Angle Side

(ii) SSS = Side Side Side

(iii) ASA = Angle Side Angle

(iv) AAs = Angle Angle Side

(v) RHS = Right angle Hypotenuse Side

**(i) SAS (Side Angle Side):** 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.

**(ii) SSS (Side Side Side) **: If three sides of one triangle are equal to three of the other triangles, then the two triangles are congruent.

**(iii) ASA (Angle Side Angle: **If two angles and the included side of one triangle are equal to two angles and the included side of the other triangle, then the two triangles are congruent.

**(iv) AAS (Angle Angle Side: **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.

**(v) RHS (Right angle Hypotenuse Side): **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 .

**Properties of Triangles**

(i) Angles opposite to equal sides of an Isosceles triangle are equal.

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

**Inequalities in triangles**

(i) In a triangle, angle opposite to the longer sides is larger (greater).

(ii) In a triangle, side opposite to the larger (greater) angle is longer.

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