Right angle theorem
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Two angles are right angles if they are both supplementary and congruent to each other. The Right-Angle Theorem states that if two angles form a straight line and are congruent, then they must each measure 90 degrees and be right angles. The proof shows that two angles <1 and <2 that are supplementary and congruent must each measure 90 degrees by using the definitions of supplementary, congruent, and right angles.
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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 DIAGRAM Supplementary
- 3. Theorem : If two angles are both supplementary and congruent, then they are right angles. 1 2 IF 1 2 then 1, 2 are right angles by RAT1
- 4. Proof 1 2 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