So far you have been working primarily with interior angles of triangles; angles on the inside of a triangle. When one side of a triangle is extended, an exterior angle is formed.

  • An exterior angle and its adjacent interior angle will sum to 180° because they both lie on a straight line.
  • An exterior angle is equal to the sum of the non-adjacent interior angles in the triangle. For the following diagram, a + b = c. Can you explain why this is true? You will prove this statement in your assignment.

Example 2

Prove that .

Proof:

∠ABC and ∠CBD are supplementary, so

∠AEF is an external angle to ΔADE, so

Corresponding angles ∠ABC and ∠ADE are equal so .



For further information about angle properties of triangles see pp. 87–89 of Principles of Mathematics 11.