Prove that the interior angles of a triangle have a sum of 180º Objective Prove that the interior angles of a triangle have a sum of 180º

Step 1 You need to remember that angles on a straight line add up to 180º. Let’s call this Fact 1

a Step 2 You need to remember that alternate angles are equal. Let’s call this Fact 2

Step 3 Draw two parallel lines

Step 4 Draw two lines within the parallel lines to create a triangle.

Step 5 Label the angles inside the triangle. a b c

Step 6 Now, use Fact 2 to label the alternate angles which are the same as b and c a b c b c

Step 7 Finally, notice that a, b and c form a straight line. Fact 1 tells us that a + b + c = 180º

We have proved … … that the interior angles in any triangle have a sum of 180º.