Investigate the relationship between the three interior angles in a triangle. (i) Work with a classmate to draw any triangle.
(ii) Using a protractor, fi nd the measure of each of the three interior angles. Find the sum of these angles.
(iii) Tear the three corners off the triangle and place them together. What is the measure of the angle they form?
(iv) Repeat this activity for two more triangles. What have you discovered about the three interior angles?
B
Labelling a triangle The sides are labelled using lower case letters.
The points where two sides of a triangle meet is called a vertex of the triangle and are labelled using capital letters.
The angles are labelled using capital letters. A triangle can be named by listing the vertices in the order that you meet them, as you go around the shape. You can start at any vertex and go clockwise or anti-clockwise, e.g. the triangle here could be named using the three vertices ∆ABC.
c b A A
Theorem (4) The angles in any triangle add to 180 degrees |∠A| + |∠B| + |∠C| = 180 0
Proof of Theorem 4 The angles in any triangle add to 180 degrees.