G-CO.12 Construction #2. Copying an Angle.

Given angle ABC, copy the angle using only a compass and straightedge.

Steps. 1. Draw ray DE. (Do this away from the figure.) 2. Draw point F on ray BC between B and C. 3. Use a compass to draw an arc centered at B that intersects rays BA and BC at points F and G. 4. Draw an arc with the same compass measurement as step 3, but centered on D that intersects ray DE at H. 5. Use a compass to measure an arc (and draw the arc) centered at G that goes through F. 6. Use a compass to draw an arc with the same measurement as step 4, centered at H, intersecting the arc from step 3 at point I. 7. Draw ray DI.

What is true about the two angles? How do you know?