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Geometry Notes

Geometry Notes. Sections 2-8. What you’ll learn. How to write proofs involving supplementary and complementary angles How to write proofs involving congruent and right angles. Vocabulary. Adjacent Angles Congruent Segments Angle Addition Postulate Segment Addition Postulate Midpoint

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Geometry Notes

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  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 • Adjacent Angles • Congruent Segments • Angle Addition Postulate • Segment Addition Postulate • Midpoint • Segment Bisector • Angle Bisector • Opposite Rays • I hope so. . . . • There is no new vocabulary • However. . . Do you know these definitions. . .? • Supplementary Angles • Complementary Angles • Reflexive Property • Symmetric Property • Transitive Property • Perpendicular lines • Linear Pair of Angles • Vertical Angles • Congruent Angles

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

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

  6. 2 1 Supplement Theorem • If two angles form a linear pair, then they are supplementary. • two angles form a linear pair, they are supplementary • 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.

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

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

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

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

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

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

  13. 2 1 More theorems. . . • Complement theorem • If the noncommon sides of two adjacent angles form a right angle, then the angles are complementary angles. 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

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