Solving Special Right Triangles: 30°-60°-90° and 45°-45°-90°

For sure you have read about special right triangles, and how it is stated that the side opposite to the 30° angle helps to define the other two sides in a 30°-60°-90°, and the legs in a 45°-45°-90° are used to define the hypotenuse; but you still don't know why this is true!

You will learn in this lesson why, and how you may remember it in the future. We start with an equilateral triangle to find the 30°-60°-90° side relationship, and we continue with a square to find the 45°-45°-90° side relationship; this way you will interiorize in your mind the concepts and they will come to you whenever you need them again in a problem solving process! When a similar version is given to solve, to work it on the screen you will use your stylus and the marker tools menu.

Lesson's Content

Lesson In PDF Format (no animations)


Lesson's Glossary

Acute triangle
A triangle whose angles are acute.


Altitude of a triangle
The perpendicular segment from a vertex to the line containing the opposite side of a triangle.

Angle bisector
A ray that is in the interior of an angle and forms two equal angles with the sides of that angle.


Corresponding Parts of Congruent Triangles are Congruent.

Equilateral triangle
A triangle whose sides are equal in length.

Isosceles triangle
A triangle with two sides of equal length.

The segment connecting the vertex of an angle in a triangle to the midpoint of the side opposite it.

Obtuse triangle
A triangle with one acute angle.

Perpendicular bisector
The bisector of a segment perpendicular to it.

Right triangle
A triangle that has a 90 degree angle.

Scalene triangle
A triangle with no equilateral sides.

A polygon with three sides.


Didn't you find what you were looking for? Do your search here!