Angles of Triangles

Essential Question: How does the angle sum theorem help you find the measures of missing angles in triangles?

I can use theorems, postulates and/or definitions to prove theorems about triangles including: measures of interior angles of a triangle sum to 180 degrees

Triangle Angle Sum Theorem

The sum of the measures of

the angles of a triangle is 180

degrees

Let’s try to understand why this is true.

Let’s prove it. First Draw this picture, then write the proof below

The Triangle Angle Sum Theorem also leads us to another observation……

If I know two of the angles in a triangle, to find the third angle I….

CAN SET THE SUM OF THE THREE ANGLES EQUAL TO 180 AND SOLVE FOR THE THIRD ANGLE

Using the Triangle Angle Sum Theorem….

This is just an example…NOT the example from your notes…..

Triangle Exterior Angle Theorem

The measures of each exterior

angle of a triangle equals the sum of it’s

two remote (non-adjacent) interior

angles.

Now let’s try to understand why this is true. Let’s prove it. First draw this picture, then write the proof.