It means that if we are given some facts about a triangle, we can find some or all of the rest. For example, if we know two sides of a right triangle we can find (or 'solve for') the third side using Pythagoras' Theorem.

To completely solve a triangle it usually means finding everything about it - all three sides and all three angles. But often we are just interested in one unknown aspect of the triangle.

Tool | Given | You can find |

Interior angles sum to 180° | Any two interior angles | The third angle |

Pythagoras' Theorem | Two sides of a right triangle | The third side |

If you are familiar with trigonometry, the following tools can be used with **any triangle**:

Tool | Given | You can find |

Law of Cosines | Two sides and the angle between them | The third side |

Law of Sines | One side and its opposite angle, and one other item | Everything else |

Again, if you are familiar with trigonometry, the following tools can be used with **right triangles**:

Tool | Usage |

Sine | These trigonometry functions relate an angle and two other sides. If you know two of the three, you can find the other. It is beyond the scope of the this volume on Geometry to define them here. See the Trigonometry Overview for a brief description. |

Cosine | |

Tangent |

The tools listed above can be used in any combination. There is no 'right way' of solving a triangle (or any other geometric problem). Just as in woodworking, you can use the tools in many ways and in many sequences. Think about what you have been given to start, and find tools that lead you in the direction you want to go.

- 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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