45° 45° 90° Triangle
Try this In the figure below, drag the orange dots on each
vertex to reshape the triangle.
Note how the angles remain the same, and it maintains the same proportions between its sides.
This is one of the 'standard' triangles you should be able recognize on sight. A fact you should commit to memory is:
With the being the hypotenuse (longest side).
This can be derived from
Pythagoras' Theorem.
This ratio will come in handy later in the study of trigonometry. In the figure above, as you drag the vertices
of the triangle to resize it, the angles remain fixed and the sides remain in this ratio.
Because the base angles are the same (both 45°) the two legs are equal and so the triangle is also isosceles
Area of a 454590 triangle
As you see from the figure on the right, two 454590 triangles together make a square, so the area of one of them is half the area of the square.
As a formula
where
S is the length of either short side
While you are here..
... I have a small favor to ask. Over the years we have used advertising to support the site so it can remain free for everyone.
However, advertising revenue is falling and I have always hated the ads. So, would you go to Patreon and become a patron of the site?
When we reach the goal I will remove all advertising from the site.
It only takes a minute and any amount would be greatly appreciated.
Thank you for considering it! – John Page
Become a patron of the site at patreon.com/mathopenref
Other triangle topics
General
Perimeter / Area
Triangle types
Triangle centers
Congruence and Similarity
Solving triangles
Triangle quizzes and exercises
(C) 2011 Copyright Math Open Reference. All rights reserved
