1. Geometry Notes Sections 2-8

2. What you’ll learn How to write proofs involving supplementary and complementary angles How to write proofs involving congruent and right angles

3. Vocabulary There is no new vocabulary However... Do you know these definitions...? SSupplementary Angles CComplementary Angles RReflexive Property SSymmetric Property TTransitive Property PPerpendicular lines LLinear Pair of Angles VVertical Angles CCongruent Angles AAdjacent Angles CCongruent Segments AAngle Addition Postulate SSegment Addition Postulate MMidpoint SSegment Bisector AAngle Bisector OOpposite Rays II hope so....

4. Congruence of Segments is... Reflexive  segments Symmetric  segments Transitive  segments A segment is congruent to itself. AB  AB You can switch the left and right sides If AB  CD then CD  AB. If AB  CD and CD  EF, then AB  EF.

5. Congruence of Angles is... Reflexive  angles Symmetric  angles Transitive  angles An angle is congruent to itself.  A   A You can switch the left and right sides If  A   B then  B   A. If  A   B and  B   C, then  A   C.

6. Supplement Theorem What are we given?  Look in the hypothesis of the conditional statement and draw it. Now what can we conclude?  Look in the conclusion of the conditional statement   1 and  2 are supplementary. IIf two angles form a linear pair, then they are supplementary.  two angles form a linear pair, 1 2 they are supplementary

7. How does this work in problems? Linear pairs → supplementary → add up to 180  1 2 If  1 and  2 form a linear pair and m  2 = 67, find m  1.

8. More example problems Linear pairs → supplementary → add up to 180  Find the measure of each angle.

9. More example problems Linear pairs → supplementary → add up to 180  Find the measure of each angle.

10. Vertical Angles We’ve done this before. DDraw two vertical angles If two angles are vertical angles then they are congruent. Vert.  s →  → =

11. How does this work in problems? 1 2 If m  2 = 72, find m  1. Vert.  s →  → =

12. More example problems Find the measure of each angle. Vert.  s →  → =

13. More theorems... Complement theorem If the noncommon sides of two adjacent angles form a right angle, then the angles are complementary angles. 1 2  1 &  2 complementary → m  1 + m  2 = 90

14. More theorems... Angles supplementary to the same angle or to two congruent angles are congruent.

15. More theorems... Angles complementary to the same angle or to two congruent angles are congruent.

16. More theorems... Perpendicular lines intersect to form four right angles. All right angles are congruent. Perpendicular lines form congruent adjacent angles. If two angles are congruent and supplementary, then each angle is a right angle. If two congruent angles form a linear pair, then they are right angles.

17. Have you learned.... How to write proofs involving supplementary and complementary angles? How to write proofs involving congruent and right angles? Assignment: Worksheet 2.8A