Download Unit 3

Common Core Curriculum Map 2012-2013
Common Core Math II
Common Core Unit Name:
Unit Number: 3
Parallel & Perpendicular Lines
Enduring Understanding:
Students need to attend to precision in determining the slopes of parallel & perpendicular lines, writing equations of parallel & perpendicular lines given line & point that it
passes through in order to construct viable arguments in making sense of the problems & perservering in solving them.
Students will look for & make use of structure in using the properties of parallel lines cut by transversal to determine measures of angles formed.
Students will model mathematics by using appropriate tools & attending to precision in basic constructions such as construct a line parallel to a given line through a
given point, line perpendicular to a given line through a point on the line, line perpendicular to a given line through a point not on the line.
Students will reason abstractly & quantitatively in order to construct viable arguments & critique the reasoning of others to prove alternate interior angles &
corresponding angles are congruent when transversal crosses parallel lines
Standard
G.CO.12 Make formal geometric constructions with a
variety of tools and methods (compass and straightedge,
string, reflective devices, paper folding, dynamic
geometric software, etc.). Copying a segment; copying an
angle; bisecting a segment; bisecting an angle;
constructing perpendicular lines, including the
perpendicular bisector of a line segment; and
constructing a line parallel to a given line through a point
not on the line. NQ.2 Define appropriate quantities for the
purpose of descriptive modeling.NQ. 3 Choose a level of
accuracy appropriate to limitations on measurement
when reporting quantities.
G.CO.9 Prove theorems about lines and angles.
Theorems include: vertical angles are congruent; when a
transversal crosses parallel lines, alternate interior angles
are congruent and corresponding angles are
congruent;points on a perpendicular bisector of a line
segment are exactly those equidistant from the
segment’s endpoints.
Essential Questions
Pacing
Guideline
Can I identify the transversal in a diagram of intersecting
lines?
Can I find the measure of angles formed by parallel lines
that are cut by a transversal?
Can I set up and solve algebraic equations based on the
location of given information of angles formed by parallel
lines that are cut by a transversal?
Can I prove two lines are parallel using the converses of the
parallel line theorems?
Can I find the slope of two lines and determine that they are
parallel, perpendicular, or neither?
Can I write the equation of a line that is parallel or
perpendicular to a given line, through a given point?
How will I be able construct a parallel line through a given
point?
How do I construct a line perpendicular through a given
point on the line & a given point not on the line?
Can I write a proof to prove verticals congruent, alternate
interior angles & corresponding angles congruent when a
transversal crosses parallel lines?
8 Include day
of review &
day of test
Key Academic
Vocabulary
Transversal
intersecting lines
angle
parallel lines
converse theorem
slope
perpendicular lines;
line
point
alternate interior angles
alternate exterior angles
corresponding angles
consecutive interior angles
same side interior angles
Compass
straightedge
parallel
point
perpendicular
vertical angles
congruent
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Common Core Curriculum Map 2012-2013
Common Core Math II
G.CO.5 Given a geometric figure and a rotation,
reflection, or translation, draw the transformed figure
using, e.g., graph paper, tracing paper, or geometry
software. Specify a sequence of transformations that will
carry a given figure onto another.
NQ. 2 Define appropriate quantities for the purpose of
descriptive modeling.
NQ. 3 Choose a level of accuracy appropriate to
limitations on measurement when reporting quantities.
A.CED.1 Create equations and inequalities in one
variable and use them to solve problems. Include
equations arising from linear and quadratic functions, and
simple rational and exponential functions.
A.CED.3 Represent constraints by equations or
inequalities, and by systems of equations and/or
inequalities, and interpret solutions as viable or nonviable
options in a modeling context. For example, represent
inequalities describing nutritional and cost constraints on
combinations of different foods.
G.PE.5 Prove the slope criteria for parallel and
perpendicular lines and use them to solve geometric
problems (e.g., find the equation of a line parallel or
perpendicular to a given line that passes through a given
point).
Common Core Unit Name:
2
Common Core Curriculum Map 2012-2013
Common Core Math II
Unit Number:
Location of these resources
Suggested Resources by Unit
Notebooks, pen/pencil, property practice worksheets, McDougal Littell
Geometry Text Book, 2004 edition. McDougal Littell Resources, 2004 edition.
pencils, rulers, compass, paper & directions of how to do the constructions.
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