Constructing a 45-degree AngleDate: 06/02/98 at 15:15:23 From: Tiger Lily Subject: Constructing a 45-degree angle without a protractor Dr. Math: This is probably an easy question but I can't find an explanation in my math book. How do you construct a 45-degree angle with only a compass and a straightedge? I know how to copy and bisect angles with only a compass and a straightedge. But how do I actually make a specific degree angle? Please help. Tiger Lily Date: 06/15/98 at 19:34:16 From: Doctor Jeremiah Subject: Re: Constructing a 45-degree angle without a protractor Hi. To create an angle of 45 degrees we need two lines that intersect at a 45-degree angle. One way of doing this is to create a 90-degree angle and bisect it. This requires only a compass and straight edge. To create a 90-degree angle we need an original line that has another line perpendicular to it. This requires only a compass and straight edge. To create a perpendicular line we need to create two points to draw the line through. Step 1: Draw the original line --------A-----------------B---------- Step 2: Mark temporary arcs from point A \ \ \ --------A-----------------B---------- / / / Step 3: Mark temporary arcs from point B \ / X / \ --------A-----------------B---------- \ / X / \ Step 4: Draw a line through the points \|/ X /|\ | | | | |90 --------A--------+--------B---------- | | | | | \|/ X /|\ Now we have the right angle we need to bisect to make a 45-degree angle. The only difference between bisecting a 45-degree angle and what we just did is that we don't need to draw two sets of marks. We only need to draw one set of marks because the intersection between the original line and the perpendicular line is the other. So now we draw a line through the cross we just drew and the intersection and we get: | | + | | + C --+-- | + | | + | + | + 45 +---------B---------- -Doctor Jeremiah, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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