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Perpendicular at the endpoint of a ray
Geometry construction using a compass and straightedge
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After doing this |
Your work should look like this |
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Start with a given ray. |
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| Step 1 |
Pick a point not on the line, about 6 cm from the endpoint of the ray.
Its exact location is not important. Label it D. |
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| Step 2 |
Set the compass on point D and set its width to the endpoint of the ray. |
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| Step 3 |
Draw an arc that crosses the ray and extends over and above the ray endpoint.
(If you prefer, draw a complete circle.) |
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| Step 4 |
Draw a diameter through D from the point where the arc crosses the ray. |
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| Step 5 |
Draw a line from the ray's endpoint to the endpoint of the diameter line |
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| Step 6 |
Done. The last line drawn is perpendicular to the ray. |
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Why it works
This construction works as a result of
Thales Theorem.
From this theorem, we know that a diameter of a circle always subtends a right angle to any point on the circle.
In this construction we:
- Create a circle that has the end part of the given ray as a chord. (step 3).
- We then draw a diameter of the circle (step 4).
- When we close the triangle in step 5, we know it must be a right triangle from Thales Theorem.
Try it yourself
Click here for a printable worksheet containing two problems to try.
When you get to the page, use the browser print command to print as many as you wish. The printed output is not copyright.
Constructions pages on this site
Lines
Angles
Triangles
Triangle Centers
Circles, Arcs and Ellipses
Polygons
Non-Euclidean constructions
(C) 2009 Copyright John Page
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