Triangles

Know the angle sum (180°), the Pythagorean theorem, the common right triangles, and that similar triangles have proportional sides.

How to do it

In a right triangle, a² + b² = c², where c is the side across from the right angle.
Spot the families: 3-4-5 (and 6-8-10), 5-12-13, 8-15-17.
Special triangles: 45-45-90 has sides x, x, x√2; 30-60-90 has sides x, x√3, 2x.
Similar triangles: set up a ratio of matching sides.

Example

Q. A right triangle has legs 6 and 8. How long is the hypotenuse?

Answer 10

It is a 3-4-5 triangle doubled. Or 36 + 64 = 100, and √100 = 10.

Traps

Using a² + b² = c² when the triangle has no right angle.
In a 30-60-90 triangle, putting x√3 across from the 30° angle. The shortest side is across from the smallest angle.

Practice it

Every practice question comes with a full explanation, including why each wrong choice is wrong. Free, with no account.