A median in a right triangle | plane geometry | elementary level

Episode 52.

A median in a right triangle | plane geometry | elementary level.

Branch of mathematics: plane geometry.
Difficulty level: elementary.

Theorem. A median in a triangle is equal to half of the opposite side if and only if it is a right triangle with the right angle at the vertex from which the median is drawn.

A differently phrased statement of the same theorem:
Theorem. A median $BM$ in a triangle $ABC$ is equal to $\frac{1}{2}AC = AM = MC$ if and only if $\angle{ABC}=90^{\circ}$.

Mathematics. Geometry. Plane geometry.
#Mathematics #Geometry #PlaneGeometry

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