Construction #2. Copying an Angle.

Given angle ABC, copy the angle using only a compass and straightedge.
Steps.[br]1. Draw ray DE. (Do this away from the figure.)[br]2. Draw point F on ray BC between B and C. [br]3. Use a compass to draw an arc centered at B that intersects rays BA and BC at points F and G.[br]4. Draw an arc with the same compass measurement as step 3, but centered on D that intersects ray DE at H.[br]5. Use a compass to measure an arc (and draw the arc) centered at G that goes through F.[br]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.[br]7. Draw ray DI.
What is true about the two angles? How do you know?
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Information: Construction #2. Copying an Angle.