An angle bisector is a line or ray that divides an angle into two equal angles.
Red angle is bisected
30°
Constructing a bisector of a given angle using a compass and a straight edge
1
Draw ∠A, as shown. Place the compass at A. Draw an arc that intersects both arms of the angle. Label the intersections B and C.
C A 3
Keep the same compass setting. Place the compass at B. Draw an arc such that it intersects the arc drawn in Step 2. Label the intersection of the two arcs G.
C G A A B C G
Worked example (i) Estimate and draw a sketch of an angle that measures 40° . (ii) Draw the angle accurately using a protractor. (iii) Name the type of angle that you have just drawn.
A
Solution (i)
(ii) B 4
Use a straight edge to draw a line through A and G.
C G 2
Reduce the width of the compass slightly and place the compass at C. Draw an arc.
1 30°
Bisector 60°
C G
[AG] bisects ∠A. Therefore |∠GAC| is A equal to |∠GAB|B