Day 1: Complementary &

Supplementary Angles

Analytic GeometryUnit 1: Similarity, Congruence &

Proofs

LSAT Logic GameA 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:

O Nicks was ranked higher than Lennon but lower than Simon.

O Prince was ranked lower than both Mitchell and Jackson.O Wonder was ranked lower than Nicks.O Jackson was ranked higher than Simon.O Nicks was ranked higher than King.

LSAT Logic GameO Nicks was ranked higher than Lennon but lower than Simon.O Prince was ranked lower than both Mitchell and Jackson.O Wonder was ranked lower than Nicks.O Jackson was ranked higher than Simon.O 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

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.

Properties of Equality

Let a, b and c be any real numbers.

Addition Property If a = b, then

Subtraction Property If a = b, then

Multiplication Property If a = b, then

Division Property If a = b and c ≠ 0, then

Reflexive Property

Symmetric Property If a = b, then

Transitive Property If a = b and b = c, then

Substitution Property If a = b, then b can replace a in an expression.

a + c = b + c

a - c = b - c

a c = b c

a⁄c = b⁄c

a = a

b = a

a = c

The Distributive Property

Use multiplication to distribute a to each term of the sum or difference within the parentheses.

Sum

Difference

a(b + c) = ab + ac

a(b - c) = ab - ac

Types of Angles

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°

Checks for Understanding

1. Can you think of a way to remember the difference between complementary and supplementary angles?

2. Can two supplementary angles both be obtuse angles? Acute angles? Why?

3. Can two supplementary angles both be right angles? Why?

Angle BisectorO A ray (or a line

or segment) that divides an angle into two congruent angles (two angles with equal measure.

Vertical Angles & Linear Pairs

linear pair: two angles that share a vertex and together they make a straight angle

vertical angles: are congruent

Checks for Understanding

O Linear pairs could be defined as being supplementary angles because they always add up to 180º. Are all supplementary angles linear pairs? Explain.