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