Step 1: Measure the distance between the points. to know the lengths of the three sides of the triangle.

FORMULA: d\ =\ \sqrt{\left(x_{2\ }-\ x_1\right)^2\ +\ \left(y_{2\ }\ -\ y_1\right)^2}\

EXAMPLE: Given points (2, 1)(10, 7),

length=\ \sqrt{\left(10\ -\ 2\right)^2\ +\ \left(7-1\right)^2}

length=\sqrt{64\ +\ 36}

Side\ length=\sqrt{100}

Step 2; Compare the given lengths of the sides and angles.

Step 3: Conclude that the given triangle is an Equilateral triangle. If you find either all lengths or all angles are equal. (Otherwise go to the next step.)

            EXAMPLE:  Lengths  36 cm, 36 cm and 36 cm   \degree

                                Angles : 60 \degree , 60 \degree and  60 \degree

Step 4:  Conclude that the given triangle is an Isosceles triangle. If you find either two equal. (Otherwise go to the next step.)

                EXAMPLE:  Lengths: 36 cm, 36 cm and 57 cm

                                    Angles: 50 \degree , 50 \degree and 80 \degree

Step 5: Conclude that the given triangle is a Scalene Triangle. If you find either sides or angles are not equal.

                EXAMPLE: Lengths: 4.6 cm, 3.4 cm and 4.3 cm

                                    Angles: 70 \degree , 30 \degree and 80 \degree