Triangle Congruence
What parts make triangle congruent?
Two triangles are congruent if the three corresponding sides are congruent and the three corresponding angles are congruent. In some cases, we know that two triangles are congruent by using only a few of these six checks.
This GeoGebra model can be used to determine what minimum information is needed to show triangles are congruent. The model has a triangle ABC which you can make into any possible triangle simply by adjusting the vertex B. In addition, there 4 segments and three angles that can be moved around. 3 of the segments always equal the length of a side of triangle ABC. The fourth can be made into any length. The three angles always have the same measure as angles in triangle ABC. Notice that you can also set the length of one leg of each of these angles. Try moving point B around and see how the segments and angles change. The segments and angles can be moved around by right-clicking points of the segments or angles or segments of the angles and dragging or rotating them.
Create a triangle that is congruent to the one provided. Record what parts you used.
Triangle Congruence
Questions to consider.
1) How many parts need to be congruent for all parts to be congruent?
2) Does the order of the parts matter?
3) Can you give instructions to someone else to create the triangle?