Do the givens.
Draw base of angle by clicking twice in drawing pad. Point A

Point B
a=Segment[A,B]

Draw top of angle by clicking once on first point A and then above the base. Point C

b=Segment[A,C]

Label: Use right-click to hide/show labels on endpoints and segment.
Draw angle marker by clicking on points B, A and C. Angle α=Angle[B, A, C]
Decorate: Right-click on angle, choose "Properties", basic tab: Show Label=Name, style tab: size=50. Click on Close.
Draw line segment by clicking twice in drawing pad. Point D

Point E
c=Line[D,E]

Label: Use right-click to rename D -> P and to hide point E.
Copy the angle.
Draw circle with radius the base of the angle and center P by clicking on points A, B and P. Circle d=Circle[P, Segment[A, B]
Draw point D by clicking on 2nd intersection point of circle and line. C=Intersect[c, b, 2].
Draw circle with radius the top of the angle and center P by clicking on points A, C and P. Circle e=Circle[P, Segment[A, C]
Draw circle with radius the segment BC and center P by clicking on points B, C and E. Circle f=Circle[E, Segment[B, C]
Draw point F by clicking on top intersection point of circles e and f. F=Intersect[e, f, 1].
Draw new angle base segment by clicking on points P and E. g=Segment[P,E]
Draw new angle top segment by clicking on points P and F. h=Segment[P,F]
Decorate: Right-click on any circle, choose "Properties", style tab: line style=dotted.

In left pane of Properties window, select other circles and repeat: line style=dotted.
In left pane of Properties window, select line c and change: line style=dashed.
Click on Close.

Draw angle marker by clicking on points B, A and C. Angle β=Angle[E, P, F]
Decorate: Right-click on angle β, choose "Properties", basic tab: Show Label=Name, style tab: size=50. Click on Close.
Check construction.
Click and drag endpoints of ends of angle to change its size. Copied angle should match changes.
See construction protocol (Command: View -> Construction Protocol)
Save construction. Command: File -> Save.
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Page last modified on May 25, 2009, at 06:16 AM