**EMAT
6700**

**by
Brad Simmons**

**Constructing Congruent Angles**

Use geometer's sketchpad to construct congruent angles.

1. Start by constructing angle P on your sketch. Select point P. Construct a ray with point P as the endpoint. Select point P again. Construct another different ray with point P as the endpoint.

2. Construct a ray with its endpoint T. Construct a point R on one ray of angle P.

3. Select point P and point R. Construct segment PR. Select point P and segment PR. Construct circle with center and radius. Select point T and segment PR. Construct circle with center and radius.

4. Select circle P and the top ray of angle P. Construct point of intersection and name it point Q. Select point R and point Q. Construct segment QR.

5. Select the ray with endpoint T. Select circle T. Construct point of intersection and name it point S. Select point S and segment QR. Construct circle with center and radius.

6. Select circle T and circle S. Construct point of intersection and name it point U. Select point T and point U. Construct ray TU.

7. Select segment PR, segment QR, circle P, circle T and circle S. Hide objects.

8. Angle UTS is congruent to Angle QPR by construction. Drag ray PQ in order to change the size of angle QPR. Angle UTS should stay congruent to angle QPR. Use the measure angle feature of geometer's sketchpad to show the angles have equal measures and remain equal after a drag.