Triangles and Trigonometry
Introduction
Properties of Triangles
Midsegments and Similarity
Triangle Congruence
Pythagoras’ Theorem
Isosceles and Equilateral Triangles
Trigonometry
Sine and Cosine Rules

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Triangles and TrigonometryMidsegments and Similarity

Reading time: ~5 min

A midsegment is a line segment that connects the midpoints of two sides of a triangle. Draw the three midsegments of this triangle.

As you can see, the midsegments split the triangle into four smaller triangles.

It turns out that all of these smaller triangles are – even the upside down one in the middle. They are also all to the original triangle, with a scale factor of 12.

This allows us to deduce some important facts about the midsegments of triangles:

Midsegment Theorem
A midsegment of a triangle is parallel to its opposite side, and exactly half the length of that side.

COMING SOON – More on triangle midsegments, and how they relate to similarity and proportionality.