EMAT 6700

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.