[Geometry- Unit 1-Parallel & Perpendicular Lines]
Enduring understanding (Big Idea): Students will be able to apply and understand the structure (properties) and
relationships between points, lines, planes, and angles.
Essential Questions:
1) What are the undefined terms in Geometry?
2) How can you describe the attributes of a segment or angle?
3) How do you prove that 2 lines are parallel or perpendicular?
BY THE END OF THIS UNIT:
Students will know…
1) distance and midpoint formulas
2) angle relationships formed by intersecting lines
Vocabulary:
1) Undefined terms
2) transversal
3) special angles formed by intersecting lines
Students will be able to…
 Find the lengths of a line segment
 Find the midpoint of a line segment
 Determine angle relationships of intersecting lines
 Write linear equations of parallel & perpendicular lines
 Interpret slopes of parallel and perpendicular lines
 Prove lines parallel or perpendicular
Unit Resources
Learning Task:
Parallel and Perpendicular Lines using Patty Paper
Parallel lines cut by a transversal using cabri jr
Mathematical Practices in Focus:
TI: Points, Lines, and Planes
2) Model with mathematics
Performance Task: Pearson Text Online (Ch 1
performance task)
3) Attend to precision
Unit Review Game:
 Geometry BINGO
1) Make sense of problems and persevere in solving them
[Geometry- Unit 1-Parallel & Perpendicular Lines]
CORE CONTENT
Cluster Title: Proving angle relationships and using them to solve problems
Standard: 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;
Concepts and Skills to Master
 Classify/determine angle relationships
 Argue with justification that vertical angles are congruent.
 Argue with justification that, when parallel lines are cut by a transversal, pairs of alternate interior angles are congruent,
pairs of alternate exterior angles are congruent, and pairs of same-side interior angles are supplementary.
 When given parallel lines, calculate angle measures and solve for variables
 When given angle measures, determine which lines, if any, are parallel
SUPPORTS FOR TEACHERS
Critical Background Knowledge
 Ability to solve equations
 Basic knowledge of parallel and perpendicular lines
Academic Vocabulary
Transversal, Alternate Interior/Exterior angles, Corresponding angles, Same-side Interior angles, Skew lines, Parallel planes
Suggested Instructional Strategies
Resources
 Formal and informal proofs do not have to be introduced
 Textbook Correlation: 2-6, 3-1, 3-2, 3-3, 3-4
at this point. Students can argue with justification by
 Angle Hunter Video
completing short answer/open-ended questions such as
“John says that consecutive interior angles are congruent
when lines are parallel. How would you convince John
that that these angles are actually supplementary?”
 The “Build a City” project or similar activity is suggested
as a real-world application follow-up assignment to assess
student understanding.
[Geometry- Unit 1-Parallel & Perpendicular Lines]
Sample Formative Assessment Tasks
Skill-based task
 Lines a and b are parallel.
o Solve for x.
o Solve for y.
o Find the measures of angles 1-5.
 Based on this information, are lines c and d
parallel? In complete sentences, explain why or
why not.
Teacher Created Argumentation Tasks (W1-MP3&6)
Problem Task
 Marie is building a sandbox in her back yard.
o Only equipped with the tools to measure angles, how
can Marie determine whether both pairs of opposite
sides are parallel?
o If both pairs of opposite sides are parallel, and one
of the angles measures 85 degrees, what are the
measures of the remaining angles?
[Geometry- Unit 1-Parallel & Perpendicular Lines]
CORE CONTENT
Cluster Title: Complete geometric instructions
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.
Concepts and Skills to Master
 Complete basic geometric constructions using a variety of tools and resources.
SUPPORTS FOR TEACHERS
Critical Background Knowledge
 Knowledge of parallel and perpendicular lines, angle bisector, perpendicular bisector
Academic Vocabulary
Transversal, Alternate Interior/Exterior angles, Corresponding angles, Same-side Interior angles, Skew lines, Parallel planes
Suggested Instructional Strategies
Resources
 Completing constructions can be used as a follow up
 Textbook Correlation: 1-6, 3-6
activity or as an investigation.
 Investigation Activity (from CMS Curriculum
o If used as an investigation, provide students with
Guide)
open-ended follow up questions to help them draw
http://math.springbranchisd.com/high/classes/algebra_one/L
accurate conclusions. For example, after giving
aying%20The%20Foundation/Lessons/Parallel%20and%20
students instructions for constructing an angle
Perpendicular%20Lines%20187-188.pdf
bisector, pose the following: “Fold your patty
paper along this line. What can you conclude about
each angle? Which of the vocabulary terms from
this section have you just constructed?”
[Geometry- Unit 1-Parallel & Perpendicular Lines]
Sample Formative Assessment Tasks
Skill-based task
 Using patty/tracing paper, pencil, straight edge, and
compass, complete the following constructions
o Parallel lines
o Perpendicular lines
o Perpendicular bisector
o Angle bisector
Teacher Created Argumentation Tasks (W1-MP3&6)
Problem Task
 Jessica is studying architecture at the University of North
Carolina at Charlotte. For homework, she must find the
center point of a regular pentagon by connecting all of the
angle bisectors. Unfortunately, Jessica has her straight
edge, but has lost her protractor. What step by step
instructions would you give to Jessica to help her complete
the assignment?
[Geometry- Unit 1-Parallel & Perpendicular Lines]
CONTENT
Cluster Title: Parallel Lines and Angle Relationships
Standard : G-MG.1 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree
trunk or a human torso as a cylinder).
Concepts and Skills to Master
 Identify parallel, perpendicular, and skew lines and parallel planes
 Identify angle relationships formed by two lines and a transversal
 Use properties of parallel lines to find angle measures
 Prove that lines are parallel using theorems about parallel lines
SUPPORTS FOR TEACHERS
Critical Background Knowledge
 Ability to properly identify and name an segment, lines, angle, and plane
 Ability to understand how an angle is formed
Academic Vocabulary
Parallel lines, skew lines, parallel planes, transversal, alternate interior angles (AIA), alternate exterior angles(AEA),
corresponding angles(CA), same side interior angles(SSI)
Suggested Instructional Strategies
Resources
 Discuss angle relationship terms as it relates to the
 Textbook Correlation: 3-1, 3-2
parallel lines and transversal. For example,
 Online Teacher Resource Center 3-1 Game: Name It –
alternate interior angles alternate across the
Claim It (Suggestion, enlarge the four diagrams on an 8 x 10 and allow
students more room to play with their die or number cube)
transversal on the inside of the parallel lines.
 Online Teacher Resource Center 3-2 Performance Task
 Allow students to use abbreviations for angle
Activity (Suggestion, enlarge the four diagrams on an 8 x 10 and allow
relationships (AI, AE, SS, C)
students more room to play with their die or number cube)
 When teaching skew lines, highlight all segments in
a rectangular prism that are not skew; thus all other
segments are skew.
[Geometry- Unit 1-Parallel & Perpendicular Lines]
Sample Formative Assessment Tasks
Skill-based task
Suppose a || b and c || d.
1. If m6 = 50, then find m11.
2. If m2 = 70, then find m6.
3. If m7= 110, then find m10.
4. If m4= 45, then find m12.
5. Which angle could you show is congruent to 11 to prove a || b?
6. What relationship between 6 and 11 shows c || d?
Teacher Created Argumentation Tasks (W1-MP3&6)
Problem Task
Have students plan and draw the street map for a fictional city
according to the directions listed below.
I. Appearance
- You will make a detailed drawing of your rough sketch
- Buildings must be placed according to the directions on the following page
- Appropriate building names must be placed on “signs” on or near the buildings
(e.g. Bank of America)
- Your name should be written in the lower right hand corner of your drawing
II. Required Items
- At the top of the drawing, place the name of the city and give it a population #
- 6 parallel streets – all named (be creative)
- 2 transversal streets that are not parallel to each other– named
- Traffic lights or stop signs at 4 intersections
- gas station and restaurant at congruent alternate exterior angles
- your house and your school at supplementary same side interior angles
- the courthouse and bank at non-congruent alternate interior angles
- a department store and a place of worship at congruent corresponding angles
- the fire department and police station at congruent alternate interior angles
- a structure/object of your choice that is skew to some part of the city
[Geometry- Unit 1-Parallel & Perpendicular Lines]
CORE CONTENT
Cluster Title: Apply properties, definitions and theorems of angles and lines
Standard 7.G.5. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to
write and solve simple equations for an unknown angle in a figure.
Concepts and Skills to Master
 Recognize angle relationships, adjacent angles, linear pairs, vertical angles, supplementary angles and complementary
angles.
 Complete simple proofs with special angle pairs.
SUPPORTS FOR TEACHERS
Critical Background Knowledge
 Students need to be able to solve algebraic equations.
Academic Vocabulary
Supplementary angles, Complementary angles, Vertical angles, Linear pairs of angles, Angle bisector
Suggested Instructional Strategies
Resources
 Have students draw intersecting lines and
 Textbook Correlation:
compare opposite angle measures and adjacent
angle measures with a compass.
 1-5 exploring angle pairs
Sample Formative Assessment Tasks
Skill-based task
Pearson Chapter one Performance task, use Task 1 or
Task 4
Teacher Created Argumentation Tasks (W1-MP3&6)
Problem Task
[Geometry- Unit 1-Parallel & Perpendicular Lines]
CORE CONTENT
Cluster Title: Measuring line segments and angles
Standard F.BF.1.a - Determine an explicit expression, a recursive process, or steps for calculation from a context.
Concepts and Skills to Master
 Apply the segment addition postulate and the angle addition postulate.
 Apply properties of lines and transversals. Identify special angle pairs.
 Recognize angle relationships, adjacent angles, linear pairs, vertical angles, supplementary angles and complementary
angles.
SUPPORTS FOR TEACHERS
Critical Background Knowledge
 Students need to be able to solve algebraic equations.
Academic Vocabulary
Supplementary angles, Complementary angles, Vertical angles, Linear pairs of angles, Angle bisector
Suggested Instructional Strategies
Resources
 Have students draw intersecting lines and
 Textbook Correlation:
compare opposite angle measures and adjacent
1-3 measuring segments
angle measures with a compass.
1-4 measuring angles
1-5 exploring angle pairs
Sample Formative Assessment Tasks
Skill-based task
Pearson Chapter one Performance task, use Task 1 or
Task 4
Teacher Created Argumentation Tasks (W1-MP3&6)
Problem Task
[Geometry- Unit 1-Parallel & Perpendicular Lines]
CORE CONTENT
Cluster Title: Basic Properties, definitions and theorems
Standard G.CO.1 Know precise definitions of angle, circle, perpendicular lines, parallel lines, and line segment, based on
the undefined notions of point, line, distance along a line, and distance around a circular arc.
Concepts and Skills to Master
 Recognize the three undefined terms in Geometry
 Apply the segment addition postulate and the angle addition postulate.
 Apply properties of lines and transversals. Identify special angle pairs.
SUPPORTS FOR TEACHERS
Critical Background Knowledge
 Students need to be able to solve algebraic equations.
Academic Vocabulary
Suggested Instructional Strategies
 Start line segment addition with integers, move
to labeled segments then expressions.
 Do the same with angle addition postulate.
Sample Formative Assessment Tasks
Skill-based task
Teacher Created Argumentation Tasks (W1-MP3&6)
Resources
 Textbook Correlation:
1-2 points, lines and plane
1-3 measuring segments
1-4 measuring angles
3-1 lines and angles
Problem Task