Download Montclair Public Schools CCSS Geometry Honors Unit: Marshall A.b

Subject
Geometry
Honors
Grade
10
Unit
Name
Overview
Angles, Lines, Proof & Constructions
Montclair Public Schools
CCSS Geometry Honors Unit: Marshall A.b
Unit # 1
Pacing
10 weeks
Students will begin by understanding the building blocks of geometry. Basic terms, theorems, and proofs will be introduced. Students will explore these
ideas by learning how to create proofs (formal and informal) and by generating constructions (using compass and straightedge, or geometric software
and other methods).
Standard #
Standard
MC,
SC,
or
AC
SLO
#
Student Learning Objectives
Depth of
Knowledge
G.CO.1
Know precise definitions of angle, circle,
perpendicular line, parallel lines, and line
segment, based on the undefined notions of
point, line, distance along a line, and distance
around a circular arc.
SC
1
Define precisely the key vocabulary – angle, circle,
perpendicular line, parallel lines, and line segment,
based on the undefined notions of point, line, distance
along a line, and distance around a circular arc.
1
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
MC
2
Calculate the measures of angles or lengths of
segments using the angle addition or segment
addition postulates.
2
3
Formally prove vertical angles congruence theorem.
3
4
Formally prove the congruent supplement / congruent
complement theorem.
3
5
Formally prove all right angles are congruent.
3
6
Apply properties of angles formed when a transversal
intersects two parallel lines (e.g. AIA, SSIA, AEA, CA)
3
7
Prove that lines are parallel given special angle
4
20132014
relationships.
G.GPE.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, find the
distance between a line and a point not on the
line, and the distance between parallel lines).
Make formal geometric constructions with a
variety of tools and methods (compass and
straightedge, string, reflective devices, paper
G.CO.12
20132014
MC
SC
8
Create an informal proof for properties of transversals
and parallel lines (e.g. alternate interior angles are
congruent, corresponding angles are congruent, sameside interior angles are supplementary)
3
9
Create an informal proof for the theorem that points
on a perpendicular bisector of a line segment are
exactly those equidistant from the segments
endpoints.)
Write an equation of a line in point-slope form and
slope-intercept form when given the coordinates of
two points, when given the line on a coordinate, or
when given the coordinates of one point and the
slope of the line.
3
11
Write the equation of a parallel or perpendicular line
when given the same criteria.
2
12
Use the distance formula for a directed line segment
(x1, y1) (x2, y2)
2
13
Calculate the distance between a line and a point not
on the line given the equation of the line and the
coordinates of the point.
3
14
Calculate the distance between two parallel lines.
3
15
Simplify complicated radical expressions without the
use of calculators
Use a compass and a straightedge to construct
a) congruent segments
b) perpendicular bisectors
2
10
16
2
2
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.GPE.6
Find the point on a directed line segment
between two given points that partitions the
segment in a given ratio.
Mathematical
Practice #
c) congruent angles
d) angle bisectors
e) parallel lines, given a line and a point not on the
line
MC
17
Calculate the midpoint of a line segment, given two
points or from a coordinate.
2
18
Find the common midpoint of diagonals in a
parallelogram drawn in a coordinate plane.
2
19
Extend the midpoint concept to calculate the
coordinates of a point that separates a line with
endpoints P1 & P2 into the ratio is a/b. Calculate the
coordinates to be ((x1+(a/b)(x2-x1)), (y1+(a/b)(y2-y1))
3
Selected Opportunities for Connections to Mathematical Practices
Big Ideas




Undefined terms (point, line, plane) are the building blocks of geometry.
Inductive and deductive reasoning are used to prove valid geometric statement true.
Geometric constructions help students discover and explore geometric concepts and interpret geometric concepts.
Parallel line properties (CA, AIA, SSIA, AEA and their converses) can be used to find missing angles and in proofs. Equations can also be used to
determine parallel and perpendicular lines
Essential Questions
• Explain the significance of undefined terms (point, line, plane) to the study of geometry.
20132014
• Why is it important to provide every logical step in a proof?
• How do you determine the measures of all the angles created by two parallel lines cut by a transversal, given only one angle’s measure?
How can you use equations of lines to determine if they are parallel or perpendicular or neither?
• What are the basic tools for a geometric construction and how does a construction differ from a measurement?
Assessments
Key Vocabulary
Construction
Coordinate
Postulate
Theorem
Transversal
Suggested Resources (list specific chapters and or page numbers from existing text that correspond to the SLOs and Standards)

Prentice Hall Geometry Textbook
Chapter 1 Sections: 1-1 (conjecture and counterexamples only), 1-2, 1-3, 1-4, 1-5, 1-6.
(Focus on problems at the end of each set of exercises.)
Chapter 2 Sections: 2-4, 2-5
Chapter 3 Sections: 3-1, 3-2, 3-5, 3-6, 3-7.
20132014