A right triangle where the
angles are 45°, 45°, and 90°.

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 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

- Triangle definition
- Hypotenuse
- Triangle interior angles
- Triangle exterior angles
- Triangle exterior angle theorem
- Pythagorean Theorem
- Proof of the Pythagorean Theorem
- Pythagorean triples
- Triangle circumcircle
- Triangle incircle
- Triangle medians
- Triangle altitudes
- Midsegment of a triangle
- Triangle inequality
- Side / angle relationship

- Perimeter of a triangle
- Area of a triangle
- Heron's formula
- Area of an equilateral triangle
- Area by the "side angle side" method
- Area of a triangle with fixed perimeter

- Right triangle
- Isosceles triangle
- Scalene triangle
- Equilateral triangle
- Equiangular triangle
- Obtuse triangle
- Acute triangle
- 3-4-5 triangle
- 30-60-90 triangle
- 45-45-90 triangle

- Incenter of a triangle
- Circumcenter of a triangle
- Centroid of a triangle
- Orthocenter of a triangle
- Euler line

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