Construction To Bisect A Given Angle

An angle bisector is a line that divides an angle into two equal parts. Let's go through the steps to construct the bisector of a given angle.

Steps of Construction:

Step 1: Draw an Arc from the Vertex

• Place the compass pointer at O (the vertex of the given angle ∠MON).

• Draw an arc that intersects the two arms (OM and ON) at P and Q.

Step 2: Draw an Arc from One Intersection Point

• Without changing the compass width much, place the compass pointer at P.

• Draw an arc inside ∠MON.

Step 3: Draw Another Arc from the Other Intersection Point

• Without changing the compass width, place the compass pointer at Q.

• Draw another arc inside the angle, making sure it intersects the arc from P at a point Z.

Step 4: Draw the Angle Bisector

• Use a ruler to draw a straight line from O to Z.

• OZ is the required angle bisector of ∠MON.

Since ∠MOZ = ∠ZON, the angle has been perfectly bisected.