This construction takes a given angle and constructs its complementary angle. Recall that the complementary angle is one that makes the given angle become 90°. So an angle of 30° has a supplementary angle of 90° - 30° = 60°.
In this construction you can extend either leg back. It will produce the same result.
This is the same drawing as the last step in the above animation.
|1||m∠FAC = 90°||Drawn at point A using the construction Perpendicular to a line at a point. See that page for proof.|
|2||m∠FAB + m∠BAC = ∠FAC||Adjacent angles|
|2||m∠FAB and m∠BAC are complementary||m∠FAB + m∠BAC = 90° See (2)|
The above animation is available as a printable step-by-step instruction sheet, which can be used for making handouts or when a computer is not available.