Definition--Triangle Concepts--45, 45, 90 Right Triangles
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Geometry >> Triangles >> Definition of a Triangle

Definition--Triangle Concepts--45-45-90 Right Triangles

45-45-90 Right Triangles

45-45-90 Right Triangles

Topic

Triangles

Definition

A 45-45-90 right triangle is a right triangle with two 45-degree angles and one 90-degree angle.

Description

The 45-45-90 triangle is another special right triangle where the two legs are of equal length, and the hypotenuse is √2 times the length of each leg. This type of triangle is also known as an isosceles right triangle due to its equal legs.

This triangle is significant in various fields, including architecture and design, where symmetry and equal angles are essential. The properties of the 45-45-90 triangle make it easy to calculate side lengths and angles, which is useful in constructing geometric shapes and solving trigonometric problems.

In math education, the 45-45-90 triangle helps students understand the concept of isosceles triangles and the relationships between angles and side lengths. It also introduces students to the Pythagorean theorem in a simplified form, as the relationship between the sides can be easily verified: 

a2 + a2 = (a√2)2

For a complete collection of terms related to functions and relations click on this link: Triangles Collection

Common Core Standards CCSS.MATH.CONTENT.4.G.A.1, CCSS.MATH.CONTENT.7.G.A.2, CCSS.MATH.CONTENT.4.G.A.2, CCSS.MATH.CONTENT.6.G.A.1
Grade Range 4 - 8
Curriculum Nodes Geometry
    • Triangles
        • Definition of a Triangle
Copyright Year 2013
Keywords triangle, defnitions, glossary