Possible Triangles

Topic:
Triangles
Given three parts of a triangle, the remaining parts can often be found. The information given is often identified by the information provided moving around the triangle. The cases are treated separately, with different applets. The cases are:
  • AAS for angle-angle-side, where a sides length is given with an adjacent angle and the opposite angle.
  • ASA for angle-side-angle, where a side and both adjacent angles are given.
  • SAS for side-angle-side, two sides and the angle between them are known.
  • SSA for side-side-angle, where two sides and an opposite angle are known.
  • SSS for side-side-side, where the lengths of all three sides are given.
Each applet illustrates one of the cases, where sliders can be used to adjust the angles and side lengths. The triangle area is shown for valid triangles and other results are indicated. If an angle is given it is represented by an orange dashed ray. One length is along the x-axis with any additional lengths represented by dashed circles. The main task is to explore the valid values for side lengths and angles for all cases.