Angle-Side-Side Intuition

Applet showing how ASS is not a valid triangle congruency theorem. The goal is to show that there exist two triangles with two congruent sides and a congruent angle that is not between them, but the third pair of sides are not congruent. Press the Magic checkbox to draw in a circle - the ray extending from point E should intersect the triangle at two points. These two points determine the two triangles which disprove this theorem. Press the First Triangle checkbox to draw in the first triangle, and the Second Triangle checkbox to draw in the second triangle. Notice that the red and blue sides are not congruent, despite two sides being congruent and an angle being congruent.