Triangle Properties & Angles

Triangles are the simplest polygon, but they are packed with powerful properties. The most fundamental one? The three interior angles always add up to 180 degrees.

Angle Sum Property

Every triangle has three angles. No matter how you stretch or squash the triangle, those three angles will always sum to exactly 180°. Use the sliders to set two of the angles — the third is forced.

Visualizing on a Graph

We can plot how the third angle changes as you adjust the other two. Below, the x-axis represents Angle A in degrees, and the curve shows what Angle C must be (holding Angle B fixed at your chosen value).

The line crosses zero when A + B = 180 — at that point there is no room left for Angle C, and the triangle degenerates into a straight line.

Types of Triangles by Angles

• Acute triangle: All angles less than 90°
• Right triangle: One angle equals exactly 90°
• Obtuse triangle: One angle greater than 90°
• Equilateral triangle: All three angles equal 60°

Special Segments in Triangles

Every triangle has three important types of internal segments:

Medians

A median connects a vertex to the midpoint of the opposite side. All three medians meet at a single point called the centroid — the triangle’s balance point. The centroid divides each median in a 2:1 ratio.

Altitudes

An altitude drops perpendicularly from a vertex to the opposite side (or its extension). All three altitudes meet at the orthocenter.

Angle Bisectors

An angle bisector splits an angle in half. All three meet at the incenter, which is the center of the inscribed circle.

Above is a triangle formed by three lines meeting pairwise, with an approximate median drawn in yellow. In a real geometry tool you would construct these precisely, but even this graph shows how the segments relate to the triangle’s shape.