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Corresponding Parts of Similar Triangles - Concept
Univ. of Wisconsin
J.D. Univ. of Wisconsin Law school
Brian was a geometry teacher through the Teach for America program and started the geometry program at his school
If two triangles are similar, then the ratio of corresponding sides is equal to the ratio of the angle bisectors, altitudes, and medians of the two triangles. To find a missing angle bisector, altitude, or median, use the ratio of corresponding sides.
If we have two similar triangles, here we have triangle abc is similar to triangle def. Then we can say that the corresponding altitudes, medians, and angle bisectors are all proportional.
So let's say that I drew in an angle bisector in triangle abc. And I call that angle bisector e, and actually I have e over here so I'm not going to use e. I'm going to use g. and then if I went over to the other triangle and I drew in an angle bisector from the corresponding vertex. I'm going to call that h. Now remember there's going to be 3 angle bisectors in each of these triangles. There's going to be 3 altitudes and 3 medians. So by making this statement we're saying that 9 different segments that correspond are all going to be proportional.
So getting back to what I was talking about, we can say that the ratio of g:h is going to be equal to the ratio of corresponding sides. So that will be equal to the ratio of c:f which would be the same thing as a:d and finally of b:e and make it an e.
So this is going to be true for the 3 altitudes, the 3 medians and for the 3 angle bisectors which you're going to use to find missing lengths and a problem on a quiz or a test.
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