EMAT 6700
by Brad Simmons
Constructing Congruent Triangles
Use geometer's sketchpad to construct a triangle that is congruent to a given triangle.
Given triangle ABC. Construct triangle XYZ congruent to triangle ABC.
1. Construct line m with point X on line m.
2. Select point X and segment AC (from triangle ABC). Construct circle by center and radius.
3. Select circle X and line m. Construct point of intersection and name it point Z.
4. Select circle X. Hide the circle. Select point X and segment AB (from triangle ABC). Construct circle by center and radius. Select point Z and segment BC (from triangle ABC). Construct circle by center and radius.
5. Select circle X and circle Z. Construct point of intersection and name it point Y.
6. Select circle X and circle Z. Hide the circles. Select line m. Hide the line. Select point X and point Y. Construct segment XY. Select point X and point Z. Construct segment XZ. Select point Y and point Z. Construct segment YZ.
Triangle XYZ is congruent to triangle ABC by construction.
Try to drag point A, B, or C in order to change triangle ABC's size. Triangle XYZ should remain congruent to triangle ABC.
Please click here for a geometer's sketchpad sketch of the figure above.