Day 1: Complementary
& Supplementary Angles
Analytic Geometry
Unit 1: Similarity, Congruence &
Proofs
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:
O Nicks was ranked higher than Lennon but lower than
O
O
O
O
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.
LSAT Logic Game
O
O
O
O
O
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
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 a + c = b + c
Subtraction Property
If a = b, then a - c = b - c
If a = b, then a  c = b  c
Multiplication Property
Division Property
Reflexive Property
If a = b and c ≠ 0, then
a⁄c = b⁄c
a=a
Symmetric Property
If a = b, then b = a
Transitive Property
If a = b and b = c, then a = c
Substitution Property
If a = b, then b can replace
a in an expression.
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 Bisector
O 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.