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 (SideSideSide) Congruence
When two triangles have corresponding sides that are congruent, the triangles are congruent.

SAS (Side AngleSide) Congruence
When two triangles have corresponding sides that are congruent, the triangles are congruent.

ASA (AngleSideAngle) Congruence
When two triangles have corresponding angles and sides that are congruent, the triangles themselves are congruent.

AAS (AngleSideAngle) Congruence
When two triangles have corresponding angles and sides that are congruent, the triangles are congruent.

RHS (RightHypotenuseSide) 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.