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Special Isosceles Triangle Properties - Concept

Teacher/Instructor Brian McCall
Brian McCall

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

In isosceles (and equilateral) triangles, a segment drawn from the vertex angle to the opposite side is the altitude, angle bisector and median. Isosceles triangle properties are used in many proofs and problems where the student must realize that, for example, an altitude is also a median or an angle bisector to find a missing side or angle.

There are a few key things that you might want to know about isosceles triangles, so we have 2 sides that are congruent and 2 base angles that are congruent that you're probably going to need for some standardized test questions or maybe even your chapter test. And that is if we draw in an angle bisector so if I bisect the vertex angle of that isosceles triangle then what we've done, is we've created 2 special types of segments. We've created a median which means this point divides this base in 2 congruent segments and we've also created altitude which is a segment from a vertex perpendicular to the opposite side. So this one segment is 3 things, it's an angle bisector as we can see from those markings, it's a median dividing the 2 pieces and it's an altitude.

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