Construct A 45 Degrees Angle
In these lessons, we will learn how to construct a 45 degrees angle by bisecting a 90 degrees angle.
We can use a similar angle bisector
method to construct some other angles from existing angles.
A 30˚ angle can be obtained by bisecting a 60˚ angle.
A 15˚ angle can be obtained by bisecting a 30˚ angle.
A 45˚ angle can be obtained by bisecting a 90˚ angle.
A 22.5˚ angle can be obtained by bisecting a 45˚ angle.
Related Topics: More Geometry Lessons
The figure shows a point A on a straight line. Construct an angle of 45˚ at point A.
Construct a 90˚ angle, and then construct an angle bisector to obtain a 45˚ angle.
Step 1 : Stretch your compasses until it is more then half the length of AB. Put the sharp end at A and mark an arc above and another arc below line segment AB.
Step 2 :
Without changing the width of the compasses, put the sharp end at B
and mark arcs above and below the line segment AB
that will intersect with the arcs drawn in step 1.
Step 3 : Join the two points where the arcs intersect with a straight line. This line is the perpendicular bisector of AB. P is the midpoint of AB.
Step 4: Bisect the 90 degree angle to form a 45 degree angle.
The following video shows how to construct a 45 degree angle using compass and straightedge. First, construct perpendicular lines (90 degrees) and then bisect that angle to get a 45 degrees angle.
Constructing a 30 degree angle
This video shows two ways to construct a 30 degree angle. The first way starts by constructing part of an equilateral triangle, then bisecting the 60 degree angle. The second method starts by constructing a rhombus with 60 and 120 degree angles, then joining the opposite vertices to leave the 30 degree angle.