compass and straightedge construction of similar triangles
Draw a line segment of length . Label its endpoints as and .
Extend the line segment past both and
Erect the perpendicular to at .
Use the compass to determine a point on the erected perpendicular such that .
Use the compass to determine a point on such that .
Note that the pictures indicate that , but the exact same procedure works if .
Connect the points and .
Note that, if , then will be between and , and will be between and . Also, if , then and .
This construction is justified by the following:
Since , we have that ;
Plugging in , , and yields that .
If you are interested in seeing the rules for compass and straightedge constructions, click on the provided.
|Title||compass and straightedge construction of similar triangles|
|Date of creation||2013-03-22 17:16:02|
|Last modified on||2013-03-22 17:16:02|
|Last modified by||Wkbj79 (1863)|