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Day 1: Complementary & Supplementary Angles

Day 1: Complementary & Supplementary Angles. Analytic Geometry Unit 1: Similarity, Congruence & Proofs. LSAT Logic Game.

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Day 1: Complementary & Supplementary Angles

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  1. Day 1: Complementary & Supplementary Angles Analytic Geometry Unit 1: Similarity, Congruence & Proofs

  2. LSAT Logic Game A panel of music historians ranked eight contemporary songwriters – Jackson, King, Lennon, Mitchell, Nicks, Prince, Simon, and Wonder – according to their relative impact on the evolution of the popular song form. No other songwriters were considered, and there were no ties in the final ranking. The ranking of the songwriters met the following conditions: • Nicks was ranked higher than Lennon but lower than Simon. • Prince was ranked lower than both Mitchell and Jackson. • Wonder was ranked lower than Nicks. • Jackson was ranked higher than Simon. • Nicks was ranked higher than King.

  3. LSAT Logic Game • Nicks was ranked higher than Lennon but lower than Simon. • Prince was ranked lower than both Mitchell and Jackson. • Wonder was ranked lower than Nicks. • Jackson was ranked higher than Simon. • Nicks was ranked higher than King. 1. Which one of the following could represent the ranking of songwriters, listed from highest to lowest? (A) Jackson, Simon, King, Mitchell, Prince, Nicks, Lennon, Wonder (B) Jackson, Simon, Prince, Nicks, Mitchell, Wonder, Lennon, King (C) Mitchell, Simon, Jackson, Prince, Nicks, Lennon, Wonder, King (D) Mitchell, Jackson, Simon, Nicks, King, Wonder, Lennon, Prince (E) Mitchell, Jackson, Prince, Simon, Lennon, Wonder, Nicks, King

  4. Reasoning in Algebra and Geometry Logical reasoning from one step to another is essential in building a proof. Reasons in a proof include given information, definitions, properties, postulates, and theorems.

  5. Properties of Equality a+ c = b + c a- c = b - c a c = b  c a⁄c = b⁄c a = a b= a a = c

  6. The Distributive Property a(b + c)= ab + ac a(b - c)= ab - ac

  7. Types of Angles

  8. Special Pairs of Angles complementary angles: pair of angles whose sum of measures equal 90° supplementary angles: pair of angles whose sum of measures equal 180°

  9. Checks for Understanding • Can you think of a way to remember the difference between complementary and supplementary angles? • Can two supplementary angles both be obtuse angles? Acute angles? Why? • Can two supplementary angles both be right angles? Why?

  10. Angle Bisector • A ray (or a line or segment) that divides an angle into two congruent angles (two angles with equal measure.

  11. Vertical Angles & Linear Pairs linear pair: two angles that share a vertexand together they make a straight angle vertical angles: are congruent

  12. Checks for Understanding • Linear pairs could be defined as being supplementary angles because they always add up to 180º. Are all supplementary angles linear pairs? Explain.

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