12.2 - Some Special Triangles

Links and useful resources

Altitude of a triangle
- The altitude of a triangle is the distance from one vertex to the opposite side (it's always perpendicular to the side, even if that means it lands outside of the triangle!)
isosceles triangles
- Isosceles triangles have two equal sides, which are called the "legs" of the triangle
- A right triangle can be isosceles, but only if two angles are 45 degrees. The hypotenuse length is then $\sqrt{2} \cdot l$ , where $l$ is the length of one of the legs.
30-60-90 right triangle
- A 30-60-90 right triangle is half of an equilateral triangle
- Its sides are in the proportion $1 : \sqrt{3} : 2$

If one leg of an isosceles right triangle has length 5, then what are the lengths of the other leg and the hypotenuse of the triangle?
If one leg of an isosceles right triangle has length 8, then what are the lengths of the other leg and the hypotenuse of the triangle?
If we know the length of one leg of an isosceles right triangle, then what’s a fast way to find the length of the hypotenuse?
Suppose $△ A B C$ is equilateral with side length $6$ . Find the length of an altitude of $△ A B C$ .
Find the area of $△ A B C$ .