A triangle has three sides and three angles. The three angles always add to 180 degree. There are three special names given to triangles that tell how many sides (or angles) are equal.

There can be 3, 2 or no equal sides/angles:

Equilateral

• Three equal sides
• Threeequal angles, always 60°

Isosceles

• Two equal sides
• Two equal angles

Scalene

• No equal sides
• No equal angles

Type of Angle

Triangles can also have names that tell you what type of angle is inside:

• Acute Triangle

All angles are less than 90°

• Right Triangle

Has a right angle (90°)

• Obtuse Triangle

Has an angle more than 90°

Test of Congruency 

These tests describe combinations of congruent sides and/or angles that are used to determine if two triangles are congruent.

• SSS (Side-Side-Side) Congruence

When two triangles have corresponding sides that are congruent, the triangles are congruent.

• SAS (Side- Angle-Side) Congruence

When two triangles have corresponding sides that are congruent, the triangles are congruent.

• ASA (Angle-Side-Angle) Congruence

When two triangles have corresponding angles and sides that are congruent, the triangles themselves are congruent.

• AAS (Angle-Side-Angle) Congruence

When two triangles have corresponding angles and sides that are congruent, the triangles are congruent.

• RHS (Right-Hypotenuse-Side) Congruence

When two right triangles have corresponding sides that are congruent, the triangles are congruent.

Isosceles triangle theorem

 The Isosceles triangle theorem states that if two sides of a triangle are congruent, then the angles opposite to these sides are congruent.

Converse of Isosceles triangle theorem

If two angles of a triangle are congruent, then the sides opposite to these angles are congruent.

For more details refer to ncert solutions for class 9 maths chapter 7 pdf.