Some Basic Types and Results of Triangles

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

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

3.  An angle whose measurement is less than {90^ \circ } is called an 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 the medians of the triangles, and the medians of a triangle 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 the ALTITUDES OF THE TRIANGLE.


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


7. Angle bisectors 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. A triangle whose one angle is {90^ \circ } is called a RIGHT ANGLED TRIANGLE.

9. A triangle whose sides are of equal length is called an EQUILATERAL TRIANGLE.

10. A triangle whose two sides or two angles are equal measurements is called an ISOSCELES TRIANGLE.

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