Question

Write a paragraph proof of the Triangle Angle Sum Theorem using the following figure. A line should pass through F as part of the proof

Answer 1

Step-by-step explanation:

Let point O be any point in the triangle. Join line segments OD, OE and OF.

There are now 3 triangles inside the triangle DEF.

Let the sum of angles in each of these triangles be x.

It follows that 3x = Sum of angles at point O + Sum of angles in triangle DEF = 360° + x.

3x = 360° + x, 2x = 360°, x = 180°.

Hence the sum of angles in any triangle is 180°.