Download Parallel Lines Task.docx

Unit Parallel Lines and Angles Performance Task
Subject GEOMETRY
Grade Level
9, 10, 11
Overarching Question(s):
How do we prove that the lines are parallel and other angle relationships based on the given information?
Common Core Learning Standards to be addressed
Prove geometric theorems
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.
Understand solving equations as a process of reasoning and explain the reasoning.
A-REI.1. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the
original equation has a solution. Construct a viable argument to justify a solution method.
A-REI.2. Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
Solve equations and inequalities in one variable.
A-REI.3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
Informational Text
Amsco Textbook: Chapter 9, page 329 - 332
http://www.regentsprep.org/Regents/math/geometry/GP8/Lparallel.htm
http://www.hippocampus.org/
Instructional Tasks
http://www.khanacademy.org/math/geometry
Part I: (Make sure to answer all parts in complete, full sentences, TYPED, on a separate sheet of paper)
1)
a) Write a brief definition for parallel lines.
b) Write a brief definition of a transversal.
c) Name the different type of angles that are created when two or more parallel lines are cut by a transversal.
Describe their relationship to each other and include a pictorial/numerical example.
2) In each exercise below, find the unknown (labeled) angles. Show all your work.
a) Find the angle marked f.
"
b) Find <j, <k and <m
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Part II: City Design Project
You are the designer of your own city. You will demonstrate your knowledge of parallel lines with a transversal and your
knowledge of angle pairs formed by the intersection of the lines.
Your city must include all of the following details to receive full credit.
1. Your city must have a name placed at the top of your project (school appropriate).
2. Six parallel streets (each street must be named and clearly labeled)
3. Two transversal streets which intersect all six parallel streets but are not parallel to each other (each street must be
named and clearly labeled)
4. One street perpendicular to any one of the transversals. (clearly named and labeled)
5. Place traffic lights or stop signs at 4 different intersections.
The following locations must be placed and clearly labeled as directed (all names must be school appropriate):
6.
7.
8.
9.
10.
A gas station and a restaurant (at alternate exterior angles)
Your home and a school (at same side interior angles)
A post office and a bank (at vertical angles)
A fire department and a police station (at corresponding angles)
A library and a park (at alternate interior angles)
The design:
•
This city can be based on your neighborhood, a neighborhood from a TV show or movie, or one that you totally
create in your head. Think outside of the box!
•
Color should be used in some form whether it is pen, marker, crayon, colored pencil, or color pictures.
•
You should use construction or graph paper to present your map OR you could create your city using a computer
and print it. Project should not be larger than 8 ½ x 11 paper.
•
Be creative & artistic as you like in drawing the buildings and roads, but remember to label each one!
Use the following checklist when designing your city:
Design:
Locations:
___ City Name placed at the top of your project
___ A gas station and a restaurant
___ At least 6 parallel streets
(at alternate exterior angles)
___ At least 2 transversals streets
___Your home and a school
___ At least 1 perpendicular street to any transversal street
___ Traffic lights or stop signs at 4 different intersections
___ Streets and buildings are drawn and labeled neat and legibly
___ Color used in some form
(at same side interior angles)
___ A post office and a bank
(at vertical angles)
___ A fire department and a police station
___ Construction/graph paper or computer designed & printed
(at corresponding angles)
___ A library and a park
(at alternate interior angles)
Parallel lines & City Design Project Rubric
Exceeds Standard
(10 pts)
Approaching Standard
(5 pts)
Does not meet
Standard
(0 pts)
Definitions & Angle
Pairs
6 terms defined
including all examples
ie. pictorial and
numerical.
3 terms have been
defined with little to no
evidence shown.
0 terms have been
defined and no evidence
has been shown
Complex parallel lines
problems
Solutions for both
problems are accurate
with appropriate work
shown
One solution and
appropriate work is
complete.
Neither problem has
been solved and/or no
appropriate work
shown.
Overall City Design
The city has a name, 6
parallel, two transversal
and one perpendicular
street all clearly named
and labeled.
The map does not
feature parallel and
perpendicular (grid)
streets. Streets are not
named..
The city does not have a
name. The map does not
feature streets.
Location of
Landmarks
Presentation,
Creativity & Neatness
The map uses
The map uses
appropriate positioning
appropriate position
based on the given angle based on the given angle
pairs for all 10
pairs for fewer than 5
landmarks.
landmarks and/or errors
are made in positioning
angle pairs.
Map is drawn neatly, is
easy to navigate, and
creativity is shown
using colors, rulers and
appropriate paper.
Map shows little to no
creativity and is messy,
but can be navigated.
This map does not
include landmarks.
Map is very messy, not
able to be navigated
with no creativity
shown.
Number of days late ______ (2pts off each day)
Example:
Points Earned
(50pts possible)
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