Select the pieces of a triangle that you believe might uniquely determine a triangle. For example, start by selecting all three sides AB, BC, and AC. Your choices will then appear in the blue workspace.
Construct a triangle by moving the elements.
- Click and drag the center dot to move the element to a new location.
- Click and drag an endpoint to rotate the element to a new orientation. The center of rotation will be the dot at the midpoint (for a side) or at the vertex (for an angle).
When two elements are aligned (that is, when two endoints, two vertices, or an endpoint and a vertex overlap), the elements will snap together. When the elements have been arranged to correctly form a triangle, all elements will snap together and the interior of the triangle will then be colored.
Once a triangle is formed with the original three elements, congruent elements will then appear to form a second triangle. The purpose is to see if congruent triangles will always be formed when using congruent elements — or is it possible to construct two triangles that are not congruent?
When a second triangle is formed, you will be asked if they are congruent. To test, click and drag within the triangle to move it to a new location, or click and drag a vertex to change its orientation. You can also use the Flip button to perform a horizontal reflection.
If the two triangles are congruent, you will be asked if it's possible to make a triangle that is not congruent to the original. Investigate more examples — don't jump to conclusions from just one example! After exploring, you should be able to conclude whether the elements you chose will always form congruent triangles or not. On the other hand, if you make two triangles that are not congruent, then no further investigation is necessary — it's clear that the elements will not always yield congruent triangles.
The Reset button will choose new sides and angles for the selected elements. The New button will remove your element selections.
