 # Special Triangles in Geometry

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A series of free, online High School Geometry Video Lessons.
Videos, worksheets, and activities to help Geometry students.

In this lesson, we will learn

• 45-45-90 special triangles
• 30-60-90 special triangles

### 45 45 90 Triangles

A 45 45 90 triangle is a special type of isosceles right triangle where the two legs are congruent to one another and the non-right angles are both equal to 45 degrees. Many times, we can use the Pythagorean theorem to find the missing legs or hypotenuse of 45 45 90 triangles. The ratio of the sides to the hypotenuse is always 1:1:square root of two.

How to find the length of a leg or hypotenuse in a 45-45-90 triangle using the Pythagorean Theorem?

### 30 60 90 Triangles

A 30 60 90 triangle is a special type of right triangle. What is special about 30 60 90 triangles is that the sides of the 30 60 90 triangle always have the same ratio. Therefore, if we are given one side we are able to easily find the other sides using the ratio of 1:2:square root of three. This special type of right triangle is similar to the 45 45 90 triangle.

How to find the legs and hypotenuse in 30-60-90 triangles when given: the short leg, the long leg, or the hypotenuse.

How to solve a 30-60-90 triangle given the length of one side?

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