# 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 $\alpha + \beta + \gamma = {180^ \circ }$