Download La Cañada Math II Advanced Newsletter Unit 2 – Parallel Lines and

La Cañada Math II Advanced Newsletter
Unit 2 – Parallel Lines and Angle Relationships
Unit 2 Overview
In this unit, students will build on their understanding of lines to
include parallelism. The unit will begin with a discussion about
parallel lines and planes. Although students will have an intuitive
sense of parallel lines from previous coursework, we will establish a
definition that can be used to determine whether or not two lines
are parallel. Students will then learn about the angles formed
when two parallel lines are cut by a transversal, and how those
angles can be classified into various pairs.
We will then resume our work with proof as we use the postulate
that corresponding angles are congruent in order to prove the
relationships that exist between alternate interior angles and same
side interior angles, as well as the effect of the transversal being
perpendicular to one of the parallel lines. In order to complete
these proofs, students will call upon previous definitions, postulates,
and properties to show the deductive process that leads to the
theorem as a conclusion. We will then explore the converse of
each of these statements and prove that, with certain given
information, the pair of lines being cut by a transversal are parallel.
The remainder of the unit will allow students the opportunity to
explore triangles and polygons using parallel lines as a jumping-off
point. Students will begin by proving that the sum of the interior
angles of a triangle is 180° by constructing a parallel line and using
a previous theorem about the relationship that exists among
angles formed when those parallel lines are cut by a transversal.
This will lead to another interesting theorem involving the exterior
angle of a triangle and its relationship to the interior angles. The
unit will conclude by exploring the sum of the angles of any
polygon, using the fact that sum of the angles of a triangle is 180°.
Students will use inductive reasoning, as described in the previous
unit, to make observations about how the interior angles of a
polygon can be calculated, and formalize that reasoning to the
general case.
Important Dates
September 20
Unit 2 Test (Tentative)
Homework Policy
Daily Homework will be assigned
and should be completed prior to
the next class meeting. For more
details about assignments, check
the class website.
Weekly Homework will be a
component of the course, and will
emphasize algebra skills learned in
last year’s course in an attempt to
maintain important ideas before
entering LC Math III.
Technology Note
We will be using various geometry
software programs this year in class.
Geometer’s Sketchpad is a
program available online, but only
in a trial capacity. In school, we will
visit the Mac Lab to use this
program. Geogebra is a free online
program that will also be useful at
home and in class.
If you are absent from a class
period in which these programs are
used, feel free to reach out to the
teacher to insure that the
assignment can be completed on
a school computer or at home
using the appropriate technology.
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Additional Unit 2 Information
Key Common Core Standards
G.CO.1 - Know precise definitions of angle, circle, perpendicular
line, parallel line, and line segment, based on the undefined
notions of point, line, distance along a line, and distance around
a circular arc.
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.
G.CO.10 - Prove theorems about triangles. Theorems include:
measures of interior angles of a triangle sum to 180°; base angles
of isosceles triangles are congruent; the segment joining midpoints
of two sides of a triangle is parallel to the third side and half the
length; the medians of a triangle meet at a point.
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.
G.CO.1 - Know precise definitions of angle, circle, perpendicular
line, parallel line, and line segment, based on the undefined
notions of point, line, distance along a line, and distance around
a circular arc.
Helpful Resources
 Geometry Textbook – Chapter 3 (Sections 1-6)
 Construction Support:
www.mathsisfun.com/geometry/constructions.html

Geogebra: www.geogebra.org
Dr. Carruthers ([email protected])
Mr. McDermott ([email protected])
Spotlight on the
Standards for
Mathematical
Practice:
MP 1: Make sense of
problems and persevere in
solving them.
Mathematically proficient
students start by explaining to
themselves the meaning of a
problem and looking for entry
points to its solution.
In this unit, students will have
the opportunity to solve
problems to which there are
several solution methods. They
will prove theorems that have a
range of methods. These
problems and theorems will
provide students with the
opportunity to analyze the
problem that they have been
given, and determine the most
appropriate path.
Describing the connection
between a diagram and the
construction of a proof or the
solution path to a problem
allows students to think
abstractly about the ideas they
are using; a skill which is
transferrable to a variety of
disciplines.
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