Triangle Sum Theorem By: Jeffrey McAven.

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Presentation transcript:

Triangle Sum Theorem By: Jeffrey McAven

Triangle What is the measure of the interior angles of a Triangle? 180°

Rectangle What is the measure of the interior angles of a Rectangle? Hint: How many triangles are there in a rectangle? 180° 180° 360° (180 for each triangle)

Does this work for ANY shape Any ideas how I might find the measure of the Interior angles for a random figure? 3 triangles 540° 4 Triangles 720°

What is the Formula? (n-2)180 = the sum of the interior angles After talking about the previous slides can you think of a possible formula? (n-2)180 = the sum of the interior angles n is the number of sides on any figure Regular polygon: all sides and angle measurements are equal.

Lets Practice shall we..... 4 Sides (4-2)180 = 360 Tell me how many triangles and what the sum on the interior angles would be. 4 Sides (4-2)180 = 360

Now what if I just tell you the amount of side?? (10-2)180 = 1,440 Decagon (10 sides) Nonagon (9 sides) Dodecagon (12 Sides) 18-gon (9-2)180 = 1,260 (12-2)180 = 1,800 (18-2)180 = 2,880