Some Basic Types and Results of Triangles

1. The angle whose measurement is of {90^ \circ } is called RIGHT ANGLE.

2. The angle whose measurement is greater than {90^ \circ } is called OBTUSE ANGLE.

3.  The angle whose measurement is less than {90^ \circ } is called ACUTE ANGLE.

4. If {A^{'}}, {B^{'}} and {C^{'}} are the midpoints of the sides of \Delta ABC, then \overline {A{A^{'}}} , \overline {B{B^{'}}} and \overline {C{C^{'}}} are called Medians of the triangles and medians of a triangles are concurrent at the point \left( {\frac{{{x_1} + {x_2} + {x_3}}}{2},\frac{{{y_1} + {y_2} + {y_3}}}{2}} \right)


5. If \overline {AE} , \overline {BF} and \overline {CG} are the perpendiculars from A, B, C to the sides (BC),  (AC) and (AB) of \Delta ABC respectively, then \overline {AE} , \overline {BF} and \overline {CG} are called ALTITUDES OF THE TRIANGLE.


6. The line passing through the mid points of the sides of \Delta , and perpendicular to the respective sides are called RIGHT BISECTORS OF THE TRIANGLE.


7. Angle bisector of a triangle are concurrent at G = \left( {\frac{{a{x_1} + b{x_2} + c{x_3}}}{{a + b + c}},\frac{{a{y_1} + b{y_2} + c{y_3}}}{{a + b + c}}} \right).


8. The triangle whose one angle is {90^ \circ } is called a RIGHT ANGLED TRIANGLE.

9. The triangle, whose sides are of equal length, is called EQUILATERAL TRIANGLE.

10. The triangle whose two sides or two angles are equal of measures, is called ISOSCELES TRIANGLE.

11. If \alpha , \beta and \gamma are the internal angles of a triangle then \alpha + \beta + \gamma = {180^ \circ }