Geometry visual reference

Special Right Triangles Chart

Special right triangles have fixed angle measures, so their side lengths always follow the same ratios. Identify the shortest leg first, then scale the entire ratio by one multiplier.

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Special right triangles chart with labeled 45 45 90 and 30 60 90 triangle diagrams side ratios and missing side examples
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How to read it

Use the chart as a decision tool.

A printable special right triangles chart with 45-45-90 and 30-60-90 diagrams, side ratios, and missing-side examples. Read the label first, identify the matching structure in your problem, then confirm that any stated conditions apply before substituting values.

01

45-45-90 triangle

An isosceles right triangle.

Side ratio

x:x:x2\displaystyle x:x:x\sqrt2

Example

7⟶72\displaystyle 7\longrightarrow7\sqrt2
02

30-60-90 triangle

Shortest leg, longer leg, hypotenuse.

Side ratio

x:x3:2x\displaystyle x:x\sqrt3:2x

Example

18⟶9, 93\displaystyle 18\longrightarrow9,\ 9\sqrt3
How to remember it

Match each side to its opposite angle

  1. 1In a 45-45-90 triangle, the legs match and the hypotenuse is leg times √2.
  2. 2In a 30-60-90 triangle, the side opposite 30° is shortest.
  3. 3The 30-60-90 ratio is x : x√3 : 2x.
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