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Geometry: Theorems

Problems

Theorems for Segments within Triangles

Theorems for Other Polygons

Problem : In what kind of triangle is the orthocenter also the circumcircle?

An equilateral triangle

Problem : In what kind of triangle is the centroid also the incircle?

An equilateral triangle

Problem : What does it say about a triangle if one of its sides is also an altitude

The triangle is a right triangle.

Problem : What must be true of a triangle if its circumcenter lies in the interior of the triangle?

The triangle must be acute.

Problem : If segments AD and BF are medians of triangle ABC, how long is segment AD?

6

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