Right angle theorem

1. Right-Angle Theorem How do you prove that two angles are right angles?

2. So…when a diagram contains a pair of angles that form a straight angle…you are permitted to write Statement Reason <1 , <2 are Supplementary DIAGRAM

3. Theorem : If two angles are both supplementary and congruent, then they are right angles. 1 2 IF then are right angles by RAT1

4. Proof Angles 1 and 2 form a straight line, so they are supplementary by Diagram <1 , <2 are congruent by given m<1 + m< 2 = 180 by def of supplementary m<1=m<2 by def of congruence m<1 + m< 1 = 180 by substitution 2m<1=180 by algebra m<1=90 by division m<2=90 by transitive <1,<2 are right angles by def of right angle 1 2