text: # Special Triangles in Geometry
  
  Related Topics:
  More Lessons for High School Geometry
  
  Math Worksheets
  
  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.
  
  Introduction to 45-45-90 Triangles
  
  ### 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.
  
  This video provides examples of how to solve a 30-60-90 triangle given the length of one side.
  
  Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.
  
  You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
metadata: {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}