Download Unit 3 parallel and perp lines

Hempfield School District Curriculum: Unit Template
Course Title: Geometry - 3273
Unit Title: Properties of Parallel and Perpendicular
Names of Teachers who Developed Unit:Gwyn,Hundley and Cunfer
Dates Developed: October 1, 2010
Approximate Dates when Taught During School Year: August –October
Approximate Number of Periods: 10
Summary: Students will build on their knowledge of angles to prove and use properties of
parallel lines. Students will learn the relationship that different forms of linear equations have
with the slopes of parallel and perpendicular lines.
Print Materials Needed: Prentice Hall – Geometry 2007, note sheets, practice sheets
Resources:
Internet Resource Links: Geometer’s Sketchpad, textbook internet links
Essential Questions (Include PA Standards, Anchors & Eligible Content)
Big Ideas: Big Ideas:
 Numbers, measures, expressions, equations, and inequalities can represent
mathematical situations and structures in many equivalent forms.
 Some geometric relationships can be described and explored as functional
relationships
 There are some mathematical relationships that are always true and these
relationships are used as the rules of arithmetic and algebra and are useful for
writing equivalent forms of expressions and solving equations and inequalities.
 Spatial reasoning and visualization are ways to orient thinking about the physical
world.
 Relations and functions are mathematical relationships that can be represented
and analyzed using words and equations.
Essential Questions:
 What are the relationships of the angles formed by two lines and a transversal?
 Does transitivity of parallel lines exist?
 Does transitivity of perpendicular lines?
 How can you prove the sum of the angles of a triangle is 180°?
 What parts of triangle are used to classify them?
 How are polygons classified?
 What formulas do you use to find the sum of the interior and exterior angles of a
regular polygon?
 What are the three forms in which an equation can be written?
 How can you write the equation of a line given two points?
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Hempfield School District Curriculum: Unit Template
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What is the relationship between the slopes of parallel lines? Perpendicular
lines?
How do you prove two lines are parallel? Perpendicular?
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Assessment Anchors:
Know
Vocabulary:
transversal, alternate
interior angles, sameside interior angles,
corresponding angles,
alternate exterior
angles,same-side
exterior
angles.Corresponding
Angles Postulate,
Alternate Interior Angle
postulates , Alternate
Exterior angle
postulate, same-side
interior angle postulate,
same – side exterior
angle postulate,
Converse of the
previous theorems,
equiangular, acurte,
right, equilateral,
isosceles, scalene
triangles. Exterior angle
of a polygon,remote
interior angle of a
polygon, triangle
exterior angle theorem,
Polygon interior angle
sum theorem, classify
polygons based on side
measure, point/slope
form, slope/y-intercept
form and standard form
of a linear equation.
slopes of parallel lines,
slopes of perpendicular
lines
Understand
Do
Students will understand: The students will be able to:
 The vocabulary
 identify angles from a
related to
diagram
Geometry
 draw conclusions about the
measurements of the above
 The applications
of this vocabulary
angles if the lines are
to algebraic and
parallel.
geometric
 Algebraic problems using
problems
AIA, AEA, CA, SSIA, SSEA
 Beginning proofs using
above theorems.
 Algebraic problems using
the converse of the above
theorems.
 Proofs using the converse of
the above theorems.
 Classify a triangle based on
its side and angle measure
 Find the remote interior or
exterior angle of a triangle
 Find the sum of the interior
angles of a triangle
 Apply the polygon exterior
and interior angle-sum
theorems
 Find the interior or exterior
angle of a regular polygon
 Identify an equation in the
slope-intercept form, point
slope form or standard form
and be able to graph from
these forms
 Determine whether lines are
parallel, perpendicular or
neither based on their
slopes.
 Write equations of parallel
and perpendicular lines.
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Hempfield School District Curriculum: Unit Template
Stage 2: Assessment Evidence
Assessments/Performance Tasks
Rubric Titles
Benchmark(s) for Course: Unit’s key Assessments
Self-Assessments
Other Evidence, Summarized
Stage 3: Learning Activities
Differentiation:
Readiness

.
Profile: Learning Styles /
Multiple Intelligences

Interest

Accommodations for ELLs:
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Hempfield School District Curriculum: Unit Template
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