# Triangles The sum of all internal angles of a triangle always add up to $180\degree$. Any triangle that does not have a right triangle is an *oblique triangle*. This includes: - **Obtuse Triangles**: a triangle with one *obtuse angle* (greater than $90\degree$) - **Acute Triangles**: a triangle with three *acute angles* (less than $90\degree$) ![[Pasted image 20250714053208.png|375]] ## Properties of Triangles All triangles can be divided into two right triangles by drawing in its **altitude**, a perpendicular line from one vertex to the opposite side ![[Pasted image 20240219232350.png|362]] ## Right Triangles > See also: > - [[Trigonometry]] A **hypotenuse** is the side of a right triangle *opposite to the right angle*. The other sides are called the **catheti/legs** of the triangle. Because of the right angle ($90\degree$), and the fact that all angles present in a triangle must add up to $180\degree$, the two remaining angles of the triangle must both be *acute angles*. ### The Pythagorean Theorem The **Pythagorean Theorem** is an equation used to get the hypotenuse or sides of a right triangle given the lengths of the other sides. - **Leg:** A side forming a right triangle - **Hypotenuse:** The side of a right triangle opposite to the $90\degree$ angle > [!summary] The Pythagorean Theorem > The sum of the square of the lengths of the legs of the right triangle is equal to the square of the hypotenuse: > $a^2+b^2=c^2$ > ![[Pasted image 20220521210539.png|300]] > If a triangle has side lengths, $a$, $b$, and $c$ and $a^2+b^2=c^2$, then the triangle is right and has a hypotenuse of $c$. ### Properties of Right Triangles ## Non-Right Triangles --- Degree Symbol (so I don’t need to keep googling it): °