Triangles - Under Construction

(the triangles - not the website)

(the triangles - not the website)

Construction 1 - For this construction we are given two sides of a triangle and the median to the third side. If we consider the sample triangle below, it will show us the way to construct a triangle with this given information.

We are given two sides, b and c, and the median to the third side. | |

GSP File |

Construction 3: Construct a triangle given the three medians.

We are given the three medians of a triangle. We also know that the medians of a triangle are concurrent in a point whose distance to a vertex is two-thirds of the length of the median from that vertex - a fact we will use in this construction. | |

To finish, we just construct the segments AC and BC and we have constructed the triangle with the given medians. Here is a link to a GSP file to see that the construction holds as the lengths of the medians are changed. |

Construction 4: Construct a triangle given two sides and the angle opposite one of the sides.

Here is a link to a GSP file for this construction. |

Construction 5: Construct a triangle given two sides and the altitude to the third side.

Given two sides and the altitude to the third side: | |

Here is a link to a GSP file for this construction. |

Construction 6: Construct a triangle given a side, the median to that side, and another median.

If we consider our sample triangle with the given information marked in red we will see a triangle that we can construct by SSS.

Here is a link to the GSP file for this construction. |

Link to free clip art used on this webpage.