Triangle Sum Theorem: The sum of the measures of the angles in a triangle is 180°.
Given: Line AB is parallel to line DE
Prove: The sum of the angles in triangle ABC = 180 degrees
Statements:
1. Draw line DE parallel to line AB
2. The measure of angle DCA + the measure of angle of BCA + the measure of angle BCE = the measure of angle DCE
3. Angle DCA is congruent to angle CAB
4. Angle BCE is congruent to angle ABC
5. The measure of angle CAB + the measure of angle BCA + the measure of angle ABC = the measure of angle DCE
6. Angle DCE = 180 degrees
7. The measure of angle CAB + the measure of angle BCA + the measure of angle ABC = 180 degrees
Reasons:
1. By Construction
2. Angle Addition Postulate
3. Alternate Interior Angles
4. Alternate Interior Angles
5. Substitution
6. Definition of Straight Angle
7. Substitution
