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Encyclopedia>Geometry>Geometric Constructions>Angles>Constructing a 90°, 45° or 22.5° Angle

Construction of 90 degree angle

Rule

Instructions for Constructing $90^{\circ}$ Angles

1.: Draw a straight line $l$ and make a point $P$ on the line.
2.: Put the point of the draft compass on $P$ and make an arc that intersects the line $l$ on both sides of $P$ .
3.: Call the intersections $A$ and $B$ .
4.: Put the point of the draft compass on $A$ and make a small arc above $P$ .
5.: Without changing the distance between the legs of the draft compass, do the same thing on $B$ . Make sure the two arcs intersect.
6.: Draw a line from the point $P$ through the point where the two small arcs intersect. This is a $90$ $^{\circ}$ angle.

Constructing a $45^{\circ}$ Angle

When you need to find an angle that is half of another angle, you always use the bisection technique. When you construct a $45$ $^{\circ}$ angle, you just bisect a $90$ $^{\circ}$ angle. You simply make a cross, midway between the two sides of the angle, with your draft compass, and draw a line from the vertex through this cross. The two new angles are both $45$ $^{\circ}$ , because $45 + 45 = 90$ .

Constructing a ${22.5}^{\circ}$ Angle

Once again, you need to find an angle that is half of another. For that reason, you can just use the bisection method one more time. So when you construct a $22.5$ $^{\circ}$ angle, you just bisect a $45$ $^{\circ}$ angle. You simply make a cross midway between the two sides of the angle with your draft compass, and draw a line from the vertex through this cross. The two new angles are both $22.5$ $^{\circ}$ , because $22.5 + 22.5 = 45$ .