**Triangles class 9** – Two or more figures are said to be congruent, if they have similar shape and size. For example: Two or more circles of same radii are congruent. Similarly, two or more squares of same sides are congruent. Consider two triangles Δ DEF and Δ MNO, if D ↔ M, E ↔ N and F ↔ O, then its congurancy is expressed symbolically, as Δ DEF ≅ ΔMNO.

**Consider triangles Δ DEF and Δ MNO:**

**Case 1: **If any two adjacent sides of the given triangles and the angle included between them are equal, then, both the triangles are said to be congruent by Side Angle Side Congruence Rule.

**Case 2: **If two angles along with the included side of both the triangles are equal, then, both the triangles are said to be congruent by Angle Side Angle Rule (AAS).

**Case 3: **If two angles and any one side of both the triangles are equal, then, both the triangles are said to be congruent by Angle Angle Side Rule (AAS).

**Case 4: **If all three sides of both the triangles are equal, then, the two triangles are said to be congruent by Side Side Side Rule (SSS).

**Case 5: **If hypotenuse and one side of two right angle triangle are equal, then, both the triangles are said to be congruent by Right Hand Side Rule (RHS).

The angle opposite to the longer side of a triangle is greater or vice versa. A triangle having two equal sides is termed as an isosceles triangle. Also, in a triangle, sides opposite to equal angles are always equal.

### Triangles Class 9 Examples

- The sum of two sides of any triangle is always greater than the 3rd side.

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