Parts of a Triangle and Special Nomenclature for Right Triangles (Montessori Geometry)

What are the parts of a triangle? What are the parts of a right-angled triangle? Learn their names below and answer the worksheets to help you remember them.

What are the parts of a triangle?

A triangle is made up of three line segments, which make up its three sides.

It also has three vertices. A vertex is the point where two sides meet. You can think of the vertices as the corners of a triangle.

The vertices are where the angles are. The three angles inside a triangle — called its interior angles — always add up to 180°.

The sides that form the angle — the ones next to it — are called the angle’s adjacent sides.

The other side — the one that’s across an angle and doesn’t form part of it — is called the angle’s opposite side.

Any side of the triangle can be chosen as its base. To make it easier to understand, the base is usually the side at the bottom — the side the triangle is resting upon — and it is usually horizontal.

The vertex opposite the base is called the apex.

The altitude or height of the triangle is the length of a perpendicular from the base to the apex.

A median is a line from a vertex to the midpoint of the opposite side. Since a triangle has three vertices and three sides, it also has three medians. The point where the three medians intersect is called the centroid of the triangle.

Did you realize?

The shortest side of a triangle is always opposite its smallest interior angle.

The longest side of a triangle is always opposite its largest interior angle.

What are the parts of a right triangle (or a right-angled triangle)?

In addition to the parts of an ordinary triangle, there are terms that are specific for right triangles (triangles with a right angle).

First of all, the right angle in a triangle is usually designated by a small square in the corner where the angle is.

The side opposite the right angle is called the hypotenuse.

The other sides are called the catheti — plural for cathetus. They are also known as the right triangle’s legs.

The longer leg is called the major cathetus.

The shorter leg is called the minor cathetus.

This is the special nomenclature (names) for the parts of a right-angled triangle.

Note on the Worksheets Below

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