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Prove that the sum of the measures of the interior angles of a triangle is 180°. Be sure to create and name the appropriate geometric figures.
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.To see why the sum of the degrees of the angles on a triangle add
to 180 look at a rectangle. It has four angles each of 90
degrees. So the sum of its angles is 360 degrees.
Draw the diagonal of this rectangle and you will split the
rectangle into two triangles. Add up all the angles of the
triangles and you should get 360 degrees since the rectangle had
360 degrees (and we didn't expand the rectangle or anything).
Your triangles are exactly alike, so they must have the same
angles in them. Call the upper triangle T1 and the lower triangle
sum of angles in T1 = sum of angles in T2.
sum of angles in T1 + sum of angles in T2 = 360.
The only possible solution is that sum of angles of T1 = sum of
angles of T2 = 180 degrees.