**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.