This page shows how to construct a perpendicular at the end of a ray with compass and straightedge or ruler. 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, so by using it in reverse we produce a right angle.
Printable step-by-step instructionsThe above animation is available as a printable step-by-step instruction sheet, which can be used for making handouts or when a computer is not available.
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:The image below is the final drawing from the animation above.
Argument Reason 1 AB is the diameter of the circle center D. A diameter is a line through the center of a circle. 2 m∠APB = 90° From Thales Theorem - the diameter of a circle subtends a right angle to any point of the circle's circumference - here P. 3 AP is perpendicular to the endpoint of the ray PB From (2)-
Q.E.D Try it yourselfClick 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. Other constructions pages on this site Lines(C) 2011 Copyright Math Open Reference.
All rights reserved
RetroSearch is an open source project built by @garambo | Open a GitHub Issue
Search and Browse the WWW like it's 1997 | Search results from DuckDuckGo
HTML:
3.2
| Encoding:
UTF-8
| Version:
0.7.4