Properties

• An exterior angle of a triangle is equal to the sum of the opposite interior angles.
  In the figure above the exterior angle ∠ABP is equal to the sum of the angles ∠BAC and ∠ACB. Adjust the triangle and convince yourself that this is always so.
• If the equivalent angle is taken at each vertex, the exterior angles always add to 360° In fact, this is true for any convex polygon, not just triangles. See Exterior angles of a polygon. In the figure below, drag the triangle's vertices and see that this is correct.

Related triangle topics

General

• Triangle definition
• Hypotenuse
• Triangle interior angles
• Triangle exterior angles
• Pythagorean Theorem
• A graphical proof of the Pythagorean Theorem
• Pythagorean triples
• Triangle circumcircle
• Triangle incircle
• Triangle medians
• Midsegment of a triangle
• Triangle inequality
• Side / angle relationship

Perimeter / Area

• Perimeter of a triangle
• Area of a triangle
• Heron's formula
• Area of an equilateral triangle
• Area by the "side angle side" method
• Area of a triangle with fixed perimeter

Triangle types

• Right triangle
• Isosceles triangle
• Scalene triangle
• Equilateral triangle
• Equiangular triangle
• Obtuse triangle
• Acute triangle
• 3-4-5 triangle
• 30-60-90 triangle
• 45-45-90 triangle

Triangle centers

• Incenter of a triangle
• Circumcenter of a triangle
• Centroid of a triangle
• Orthocenter of a triangle
• Euler line

Congruence and Similarity

• Congruent triangles

Solving triangles

• Solving the Triangle
• Law of sines
• Law of cosines

Triangle quizzes and exercises

• Triangle type quiz
• Ball Box problem
• How Many Triangles?
• Satellite Orbits