Converse of CPCTC
- I-Heng McComb
CPCTC says that corresponding parts of congruent triangles are congruent. In other words, if you know two triangles are congruent, you also know all three pairs of corresponding sides and all three pairs of corresponding angles are congruent. The converse of CPCTC says that if you have two triangles where you know all six pairs of corresponding parts are congruent, then the two triangles must be congruent. To demonstrate this idea, you will find a series of rigid motions (isometries) to map one such triangle onto another. Here is the "recipe": 1) Find a translation vector to map one vertex of the first triangle onto the corresponding vertex of the second triangle. 2) Rotate the resulting image around the vertex you have so far "matched." Adjust your angle of rotation so that one side of the first triangle lies on the corresponding side of the second triangle. 3) Finally, if necessary, reflect the resulting image across the side you have just "matched."
Map Triangle1 using rigid motions onto each of the other triangles (which all have 6 corresponding congruent parts with Triangle1). You can uncheck the checkboxes to hide the triangles you aren't using. NOTE: To make it easier to find the angle of rotation, type "RotationAngle" when asked for the angle of (CCW) rotation and then use the slider to try different angles.