Draw a linear pair of angles. Bisect each of the two angles.
Question:

Draw a linear pair of angles. Bisect each of the two angles. Verify that the two bisecting rays are perpendicular to each other. 

Solution:

Steps of construction:

1. Draw two angles DCA and DCB forming linear pair

2. With center C and any radius draw an arc which intersects AC at P and CD at Q and CB at R

3. With center P and Q and any radius draw two arcs which intersect each other at S

4. Join SC

5. With Q and R as center and any radius draw two arcs which intersect each other at T

6. Join TC

Therefore ∠SCT = 90°.   

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