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2012-13 and 2013-14 Transitional Comprehensive Curriculum
Geometry
Unit 3: Parallel and Perpendicular Relationships
Time Frame: Approximately three weeks
Unit Description
This unit demonstrates the basic role played by Euclid’s fifth postulate in geometry.
Euclid’s fifth postulate is stated in most textbooks using the wording found in Playfair’s
Axiom: Through a given point, only one line can be drawn parallel to a given line. This
axiom and several others are considered by some mathematicians to be equivalent to
Euclid’s fifth postulate. The focus is on basic angle measurement relationships for
parallel and perpendicular lines, equations of lines that are parallel and perpendicular in
the coordinate plane, and proving that two or more lines are parallel using various
methods including distance between two lines.
Student Understandings
Students should know the basic angle measurement relationships and slope relationships
between parallel and perpendicular lines in the plane. Students can write and identify
equations of lines that represent parallel and perpendicular lines. They can recognize the
conditions that must exist for two or more lines to be parallel. Three-dimensional figures
can be connected to their 2-dimensional counterparts when possible.
Guiding Questions
1. Can students relate parallelism to Euclid’s fifth postulate and its ramifications
for Euclidean Geometry?
2. Can students use parallelism to find and develop the basic angle
measurements related to triangles and to transversals intersecting parallel
lines?
3. Can students link perpendicularity to angle measurements and to its
relationship with parallelism in the plane and 3-dimensional space?
4. Can students solve problems given the equations of lines that are
perpendicular or parallel to a given line in the coordinate plane and discuss the
slope relationships governing these situations?
5. Can students solve problems that deal with distance on the number line or in
the coordinate plane?
6. Can students solve problems that deal with dividing a directed line segment
into a given ratio?
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Unit 3 Grade-Level Expectations (GLEs) and Common Core State Standards (CCSS)
Grade-Level Expectations
GLE #
GLE Text and Benchmarks
Algebra
6.
Write the equation of a line parallel or perpendicular to a given line
through a specific point (A-3-H) (G-3-H)
Geometry
12.
Apply the Pythagorean theorem in both abstract and real-life settings
(G-2-H)
16.
Represent and solve problems involving distance on a number line
or in the plane (G-3-H)
19.
Develop formal and informal proofs (e.g., Pythagorean theorem,
flow charts, paragraphs) (G-6-H)
Data Analysis, Probability, and Discrete Math
22.
Interpret and summarize a set of experimental data presented in a
table, bar graph, line graph, scatter plot, matrix, or circle graph (D-7H)
CCSS for Mathematical Content
CCSS #
CCSS Text
Congruence
G.CO.1
Know the 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.
Expressing Geometric Properties with Equations
G.GPE.6
Find the point on a directed line segment between two given points
that partitions the segment in a given ratio.
ELA CCSS
CCSS #
CCSS Text
Reading Standards for Literacy in Science and Technical Subjects 6-12
RST.9-10.3
Follow precisely a complex multistep procedure when carrying out
experiments, taking measurements, or performing technical tasks,
attending to special cases or exceptions defined in the text.
RST.9-10.4
Determine the meaning of symbols, key terms, and other domainspecific words and phrases as they are used in a specific scientific or
technical context relevant to grades 9-10 texts and topics.
Writing Standards for Literacy in History/Social Studies, Science and Technical
Subjects 6-12
WHST.9-10.1b
Write arguments focused on discipline-specific content. Develop
claim(s) and counterclaims fairly, supplying data and evidence for
each while pointing out the strengths and limitations of both claim(s)
and counterclaims in a discipline-appropriate form and in a manner
that anticipates the audience’s knowledge level and concerns.
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WHST.9-10.2d
WHST.9-10.10
Write informative/explanatory texts, including the narration of
historical events, scientific procedures/experiments, or technical
processes. Use precise language and domain-specific vocabulary to
manage the complexity of the topic and convey a style appropriate to
the discipline and context as well as to the expertise of likely
readers.
Write routinely over extended time frames (time for reflection and
revision) and shorter time frames (a single sitting or a day or two)
for a range of discipline-specific tasks, purposes, and audiences.
Sample Activities
Activity 1: Slopes and Equations of Parallel and Perpendicular Lines (GLE: 6, 22;
CCSS: G.CO.1, RST.9-10.4)
Materials List: pencil, paper, graphs of lines for work in pairs, graph paper, computer
drawing program (optional), vocabulary cards from Unit 2
Begin by having students work in pairs. Provide each pair of students with three graphs
of lines, each on a separate coordinate grid system. On one set of axes, have a graph of
parallel lines; on the other two sets of axes, have single lines with different slopes and yintercepts. Be sure to use a different set of lines for each pair of students. Provide at least
two points on each line by marking the points on the graphs. Review how to find the
slope of a line from two points, and then have students determine the slope of each of the
lines provided.
Next, have students carefully fold each of the single lines onto itself and crease the paper
along the fold line. Have students measure the angle formed by the line and the “crease”
line to confirm that it is a right angle. Be sure to engage students in a discussion that
helps them see that the “crease” line is perpendicular to the original line. Students should
develop a convincing argument that the “crease” line is perpendicular to the original lines
(i.e., The two angles are congruent because they are the same size since the angles
“match” when folded over one another. Because a line measures 180 degrees, the
measures of the two angles are 90 degrees each).
Students will then determine the slope of the “crease” line and compare it to that of the
original line. All data from the class should be recorded in a chart. The chart should
include a column for the slope of the original line and a column for the slope of the
“crease” line. Using the class data, student pairs should make a conjecture about the slope
of perpendicular lines. Review with students the process for developing the equation of
the line if two points on the line are given and have them write the equations of the given
lines and the “crease” line. Students should begin to identify characteristics of equations
of perpendicular lines to be developed further in this activity.
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Using the graph with the given parallel lines, have students fold the graph so each line
lies on itself to create a “crease” line which passes through the pair of parallel lines. Then
have students discuss how the slopes of the parallel lines are related, and whether the
“crease” is perpendicular to one or both of the given lines. This should lead to a
discussion about the theorem that states, “if a line is perpendicular to one of two parallel
lines, then it is perpendicular to the other.” Have students write the equations of the given
parallel lines and the “crease” line. Students should again begin to identify characteristics
of equations of parallel lines to be developed further in this activity.
Provide students with several equations of pairs of lines that are parallel, and several
equations of pairs of lines that are perpendicular without giving the relationships. Have
students graph the lines and determine the characteristics of the equations of the lines that
are parallel, and the characteristics of those that are perpendicular (i.e., parallel lines have
the same slopes and different y-intercepts, perpendicular lines have slopes that are
opposite reciprocals of one another). As an alternative, have students use a computer
software program like Geometer’s Sketchpad to draw a pair of perpendicular lines and a
pair of parallel lines. Have the program generate the equations of those lines and then
determine the characteristics of the equations. Have students refer to the equations they
wrote at the beginning of the activity and compare them to the equations they were given
to determine if the characteristics they have identified apply to all of the equations they
have.
Once the characteristics are determined, provide students with graphs of lines that are
parallel or perpendicular (several of each). Have students apply the characteristics of
parallel or perpendicular lines to write the equations for the given lines. Next, have
students write the equation of lines that are parallel or perpendicular to a line through a
given point on the line.
Examples:
Given that a line passes through  2,3 and  4,6  , write the equation of a line that
is parallel to the given line and passes through 1, 2  . Write the equation of the
line that is perpendicular to the original line through 1, 2  . Solution: Parallel:
1
5
y  x  ; Perpendicular: y  2 x .
2
2
To end the activity, have students working alone to write equations of any two lines that
are parallel and any two lines that are perpendicular. Do not provide them with any
information such as slopes or y-intercepts. Students should then share the equations with
a different partner. Students should graph the equations from their partner to verify that
the equations written represent parallel and perpendicular lines. Have students include
what they have learned about slopes of parallel and perpendicular lines on the vocabulary
cards (view literacy strategy descriptions) they created in Unit 2 Activity 1 to further
precisely define those terms. The information concerning the slopes can be placed in the
upper left corner with the initial definition of parallel and perpendicular lines.
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Definition/explanation:
Two lines in the same
plane that do not intersect;
two lines that have the
same slope.
Ways to name:
Line AB is parallel to Line CD;
Line AB || Line CD
parallel lines
Real-life objects:
Railroad tracks, edges
of cereal box, power
lines
Drawing:
B
A
D
C
Have students review the cards as they are working with parallel and perpendicular lines.
Students can use the cards as a study aid until they can recall the material without the aid
of the vocabulary cards.
Activity 2: Proving Lines are Parallel (GLEs: 19; CCSS: WHST.9-10.1b, WHST.910.10)
Materials List: pencil, paper, diagrams for discussion, learning log
Teacher note: The names of the special angle pairs formed by two lines and a
transversal, and the relationships of these special angle pairs are found in the Grade 8
GLEs so they are not discussed in detail here. A review may be necessary depending on
the students in the class.
Give students diagrams of parallel lines and transversals and diagrams of lines that are
not parallel with transversals. Lead a discussion to determine what characteristics of
parallel lines will guarantee that two lines are parallel (e.g., two lines are parallel if
corresponding angles are congruent, alternate interior angles are congruent, alternate
exterior angles are congruent, consecutive interior angles are supplementary, parallel
lines are everywhere equidistant).
Have students form conjectures that lead to the converses of the parallel lines theorems
(e.g., if alternate interior angles are congruent when a transversal intersects two lines,
then the two lines are parallel). Remind students that the statement, “If two parallel lines
are cut by a transversal, then corresponding angles are congruent,” is a postulate which is
accepted as true without proof. The converse, “If two lines in a plane are cut by a
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transversal so that corresponding angles are congruent, then the two lines are parallel” is
also a postulate accepted as true without proof. Using these postulates as truth, students
can prove the other theorems and converses. Allow students to initially use angle
measures to write proofs for specific sets of lines to prove these theorems, but also
require them to use general proofs that prove lines parallel through generalities. These
proofs can take any form (informal, paragraph, two-column, flow). Provide opportunities
for students to prove the other theorems which are based on the postulate for
corresponding angles. Have students complete a proof (or proofs) which involves the
theorems and/or their converses in their math learning logs (view literacy strategy
descriptions). Students should be allowed to complete any type of proof they wish as long
as they demonstrate logical thinking and reasoning and provide evidence for their
statements. The diagrams should be more than just a pair of parallel lines cut by a
transversal. The diagrams used in this proof should incorporate parallel lines in other
figures such as triangles and quadrilaterals (in a trapezoid, the angles along one leg are
supplementary; opposite angles of a parallelogram are congruent; if a segment is drawn
parallel to any side of a triangle, the corresponding angles in the similar triangles are
congruent; etc.). Students should not be asked to prove two triangles congruent at this
time, but this can serve as a precursor to the proofs they will write in Unit 4.
Example Proof:
B
F
Given:
G
H
Prove:
D
E
K
Possible Solution:
Given the measure of angle FEK, the measure of angle DEF to be
105 degrees can be found because angles DEF and FEK form a linear pair which means
the angles are supplementary (180-75 = 105). Using the given measure of angle DFE
and the measure of angle DEF, the measure of angle EDF is found to be 45 degrees
because angles DFE, EDF, and DEF are the three angles of triangle DFE and the sum of
the interior angles of any triangle is 180. Since the measures of angles GFD (given) and
EDF are equal, angle GFD is congruent to angle EDF. Angle GFD and angle EDF are
alternate interior angles. Since the alternate interior angles are congruent, line GH is
parallel to ray DK.
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Provide diagrams of two lines that are perpendicular to one line. Have students form a
conjecture that if two lines are perpendicular to the same line, they must be parallel.
Then, have students write a proof of this theorem.
To end the activity, have students respond to a SPAWN writing (view literacy strategy
descriptions) prompt using the What If? category. Have students answer the following
prompt:
Think about your favorite outing (a trip to the mall, football games, a trip to Walt
Disney World, etc.). What might your day be like if there were no way to ensure
lines are parallel?
Students responses can be included in their learning logs. After students have had time to
construct their responses, allow a few students to share their responses with the class.
Students may add their own ideas to other students’ responses or question their reasoning.
These writings could be included in a portfolio of the students’ work.
Activity 3: Distance in the Plane (GLEs: 12, 16; CCSS: RST.9-10.3, WHST.9-10.2d)
Materials List: pencil, paper, Distance in the Plane Process Guide BLM, calculator
Have students explore the distance between two points in the rectangular coordinate
system using the Distance in the Plane Process Guide BLM. This BLM will use a process
guide (view literacy strategy descriptions) to guide students through deriving the distance
formula from the Pythagorean Theorem. Process guides scaffold students’
comprehension and are designed to stimulate students’ thinking during or after their
learning. Guides also help students focus on important information and ideas making
their learning more efficient. Process guides prompt thinking ranging from simple recall
to connecting information and ideas to prior experience, applying new knowledge, and
problem-solving. This process guide gives attention to the idea that distance in the plane
between two points can be thought of as the length of a hypotenuse of a right triangle.
Thus, the Pythagorean theorem can be used to determine these distances. The guide
begins by having students recall the Pythagorean Theorem and find missing sides of right
triangles. Section B asks students to apply the concept of distance on a number line to
find the length of the legs of the right triangle and find the hypotenuse using Pythagorean
Theorem. Questions are included to prompt students’ thinking to assist students in
developing the same information. Section C asks students to generalize their work from
Section B using arbitrary points  x1 , y1  and  x2 , y2  —this is where the distance formula
is developed. Section D has students apply the distance formula to segments in the
coordinate plane. Section E gives students a real-world application to help students
connect their learning with a scenario in which they are familiar. When using the
Pythagorean Theorem and the distance formula, students are asked to simplify radical
solutions as well as use a calculator to estimate the solution. Depending on the level of
the students, discussions may need to occur as each section of the process guide is
completed to help with any misconceptions. Have students discuss their answers with a
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partner or a group to check whether they have the correct answers. Once students have
completed the process guide, lead a class discussion and have students/groups report their
thinking to the class. Have additional examples to provide students with more
opportunities to find the distance between points on the coordinate plane. Allow students
to use their process guide as needed to work through the additional examples. Encourage
students to eventually move from relying on the process guide for guidance to recalling
the information from their knowledge.
At the end of the lesson, have students reflect on their learning by answering the
following prompt in their learning logs (view literacy strategy descriptions): How are the
Pythagorean Theorem and the distance formula related? Why would a student choose to
use the distance formula over the Pythagorean Theorem? The logs should be collected at
some point and read to determine if there are any areas which may need to be clarified.
Activity 4: Dividing a Segment Into a Given Ratio on the Number Line (CCSS:
G.GPE.6)
Materials List: pencil, paper, Dividing Number Line Segments BLM
Begin with a discussion (view literacy strategy descriptions) on the following problem:
“Point D lies on
between points A and B and divides
into a ratio of 2:3. What is
the coordinate of point D?” The point of discussion is to help students improve learning
and remembering by participating in the dialog about class topics. Class discussion can
be used to promote deeper processing of content and rehearsal of newly learned content.
For this activity, use the Think Pair Square Share form of discussion. After posing the
problem above, give students some time (approximately 1 minute) to think about what
the problem means, what they know, what they need to know, and possible ways they
may attempt to answer the problem. After that time has passed, have students pair up and
share their ideas with each other. Student A should take 1 minute to share his/her ideas
and then student B should be given 1 minute to share his/her ideas. Time should also be
given for the students to talk briefly and ask each other questions to clarify their thoughts
if necessary. The third step is to have the pairs of students share with another pair (four
students, or a square). Again, each pair should be given time to give their ideas to the
other pair and vice versa. After the square has been given time to discuss, have the
students report to the entire class. Record students’ ideas for reference throughout the
lesson.
After the discussion, provide students with a copy of the Dividing Number Line
Segments BLM. Students should be guided through completing the Dividing Number
Line Segments BLM. Using the responses from the discussion, begin to identify the
correct understandings and any misunderstandings about the problem. Guide students to
understand that in order to find a point that divides the segment into a ratio of 2:3, there
must be five equal parts. Point D would then be 2 of the five parts (or 2/5 of the distance)
from point A and 3 of the five parts (or 3/5 of the distance) from point B. Using the
number line drawn on the board, demonstrate how
can be physically divided into 5
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equal parts, and then find the correct location of D. Next, show students how they can
find the point analytically (this is question 4 on the Dividing Number Line Segments
BLM)—first, find 2/5 of the length of
, then add that measure to the coordinate for A.
; D is 4 units from A so the coordinate of D is -1 + 4 = 3. Be sure to point out
that since the students are finding 2/5 of 10, they are finding the distance D is from A as
opposed to the coordinate of D since 10 is the length of the segment. Provide students
with a few more examples as needed, then have students work problems 5 and 6 on the
Dividing Number Line Segments BLM for independent practice. After the answers to 5
and 6 have been discussed, complete number 7 as a whole class. Elicit student responses
to help develop the parts of the “formula” and be sure they understand what each variable
represents. Note: The absolute value in the equation forces the distance to be positive,
and is important in this formula. In the next activity, the absolute value will be removed
because the direction of the line will produce a signed distance (which means the
expression for the distance may result in a negative value) that will be necessary to divide
the segments on the coordinate plane correctly.
Give students a few more examples and have them use the formula they just developed to
find the desired point. Be sure to revisit all ideas created through the discussion at the
beginning of the lesson and clarify any misconceptions or incorrect approaches to this
skill. As a closure, have students explain what the “formula” means, including what each
variable represents. This explanation can be written in their learning logs (view literacy
strategy descriptions) which can be collected and/or shared with the class.
Activity 5: Dividing a Directed Line Segment Into a Given Ratio on the Coordinate
Plane (CCSS: G.GPE.6)
Materials List: pencil, paper, graph paper (optional)
This activity will extend the concept of dividing a segment into a given ratio on the
number line to the coordinate plane. If the given segment is horizontal or vertical,
students can use the same intuitive thinking developed in Activity 4. However, for
directed line segments, or segments with a non-zero slope, the formula for finding the
point is not as intuitive when working with the coordinate plane, so the formula
developed in Activity 4 will be extended. The formula developed used the distance
between the endpoints on the number line. For directed segments, the formula will use
the signed distance—this means students will not take the absolute value of the distance
to find the ordered pair.
Review with students how to divide a segment into a given ratio on a number line.
 k

Remind students of the formula developed in Activity 4  1  C  A   A  . Pose the
 k1  k2

following problem: “Given AC , where A  3, 1 and C  2,5 , find B such that B
divides AC into a ratio of 1:2.” Have students think about their responses for about 30
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seconds, then share with a partner. Next, have students report to the class their thoughts
and use their responses to attempt to solve the problem. Guide them to use the formula
for the x-coordinates and the y-coordinates separately.
Solution:


1
2   3   3
3
1
  5    3
3
5
 3
3
1
4
 1 or 
3
3
XB 


1
5   1   1
3
1
B:
  6    1
3
 2 1
1
YB 
 1 
 1 ,1
 3 
Have students graph the points to see if their answer is reasonable. Then have students
find the lengths of segment AB and segment BC and verify that the ratio of AB:BC is 1:2.
Solution: AB 
61
2 61
and BC 
3
3
Next, pose the following problem to the students: “Given RT , where R  3, 4  and
T  2, 6 , find S such that S divides RT into a ratio of 2:3.” Remind students that A in
the formula should always be represented by the leftmost point. Have students use the
formula developed in Activity 4 to attempt to find S. Students should graph the point they
find to determine if it is reasonable. They will find that the point they will obtain is NOT
on the line. Ask students for their thoughts as to why that happened. Some students may
realize that they could subtract from the y-coordinate of R and get the answer. Others may
realize that they could find 3/5 of 10 (the distance from YR to YT) and add it to the ycoordinate of T. Help students understand that this formula is not efficient to find this
point. Have students work the problem again, but this time do not use the absolute value.
Students should get S  1,0 . Ask students to identify what is different about this line
segment from AC . Students should respond that segment RT has a negative slope while
segment AC has a positive slope. Explain to students that the direction is important to
help determine the correct placement of S and that removing the absolute value uses the
signed distance to determine the coordinates of S. Redefine the formula as stated below:
Given any AB and point P such that P divides AB into the ratio k1:k2, the coordinates of
k
k1
P are x p 
 xb  xa   xa and y p  1  yb  ya   ya , where  xa , ya  is the
k1  k2
k1  k2
leftmost point on the graph.
Give students more examples and have them verify that the ratio of the lengths of the two
smaller segments equal the given ratio.
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Activity 6: Parallel Lines and Distance (GLEs: 16; CCSS: WHST.9-10.2d, WHST.910.10)
Materials List: pencil, paper, computer drawing program (optional), learning log
Provide different sets of two lines. Some sets should be parallel; others should not be
parallel. These lines should be drawn on lineless paper. Ask students how they visually
determine which of the sets of two lines are parallel. Have a discussion which leads to an
understanding that parallel lines are always the same distance apart.
Lead students in a discussion about the definition of distance between a point and a line
or distance between two parallel lines. One way to do this is to draw two parallel lines on
the board and use a ruler to determine distances. Use a drawing program, such as
Geometer’s Sketchpad®, as an alternate way to demonstrate the same concept. The
discussion should reveal that the distance is always the shortest line segment between two
points (or the shortest distance between a point and a line). Have students realize that the
distance between a point and a line is the same as the length of a line segment which
starts at the point and is perpendicular to the line. To find the distance between two
parallel lines, identify a point on one of the lines and draw a segment from this point
perpendicular to the second line.
Give students diagrams on the coordinate plane and ask them to find the distance between
lines and points not on the lines. Review the concept of the Parallel Postulate here (If
there is a line and a point not on the line, then there is exactly one line that can be drawn
through the given point that is parallel to the given line).
Have students apply the concept of distance between a point and a line to polygons.
Relate the distance between a point and a line to finding the length of an altitude in a
triangle (i.e., an altitude is the perpendicular distance from a vertex to a segment on the
opposite side of the triangle). This establishes correct understandings necessary for the
concepts that will find area, surface area, and volume.
To end the activity, have the students answer the following prompt in their math learning
logs (view literacy strategy descriptions):
Describe how to determine the distance between a line and a point not on the line.
How could you use this information to help you find the distance between a plane
and a point that is not contained in that plane?
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Activity 7: Parallel Line Facts (GLEs: 19; CCSS: WHST.9-10.1b)
Materials List: pencil, paper, Parallel Line Facts BLM, ruler
Teacher Note: The focus of this activity is to apply the properties of parallel lines learned
in earlier activities. This is a good application of proof using the parallel line properties.
It also introduces information relative to angle relationships in triangles, connecting this
unit to Unit 4.
Give students copies of the Parallel Line Facts BLM and have them complete the
following steps.



Have students draw a line through one vertex of a triangle so that the line is
parallel to a side of the triangle. Have students write a proof (using parallel line
relationships from Unit 2 and earlier activities) to show that the sum of the angles
in a triangle is 180°.
Use the same diagram to write a proof to show that the measure of an exterior
angle in a triangle has the same measure as the sum of the two remote interior
angles. This the Exterior Angle Sum theorem.
Have students investigate the area of different triangles formed between two
parallel lines by moving one vertex along one of the parallel lines. Students
should recognize that the height of each triangle is always the same since the
distance between the parallel lines will not change. Since the base length doesn’t
change, students should realize that the areas are the same. Have students develop
a proof of this as well.
Sample Assessments
General Assessments



The student will create a portfolio containing samples of work completed during
activities. For instance, he/she could include the graphs from Activity 2 and
explain what happened in the activity and what was learned from the activity.
The student will respond to journal prompts that include:
o Describing at least three different ways to prove two lines are parallel.
2
o Explaining how to write the equation of a line perpendicular to y   x  5
3
through the given point (-4,6).
o Explaining the relationship between the Pythagorean theorem and the distance
formula for distance on the coordinate plane.
The student will create a “scrapbook” of pictures taken in a real-world setting (i.e.
railroad tracks) that depict parallel and perpendicular lines. This scrapbook will
include pictures and indicate how the items in the picture demonstrate the term
GeometryUnit 3Parallel and Perpendicular Relationships
3-12
2012-13 and 2013-14 Transitional Comprehensive Curriculum
chosen. The student will have a minimum of three pictures for each term. See the
Scrapbook Rubric BLM for more information.
Activity-Specific Assessments

Activity 1: The teacher will provide the student with several sets of graphs of
perpendicular lines, intersecting lines which are not perpendicular, and
intersecting lines which are almost perpendicular drawn on coordinate graph
paper. The student will use slope to determine if the lines are parallel.

Activity 1: The teacher will give each student a copy of the What’s My Line?
BLM and one of the five What’s My Line? graphs. The five graphs have different
slopes, so there is a larger probability that the students will have different
responses. The student will draw and label the x- and y-axes anywhere on the
coordinate plane that he/she chooses. Based on where the x- and y-axes are drawn,
the student will then
o find the slope of the given line and write the equation of the given line.
o write the equation for a line which passes through the given point and is
parallel
o to the given line.
o write the equation of the line which is perpendicular to the given line and
passes
o through the given point.
A What’s My Line? Rubric BLM is provided for this assessment. The What’s My
Line? BLM, the What’s My Line? Graphs, and the What’s My Line? Rubric BLM
are located at the end of the BLMs for Unit 3.

Activities 1, 3, and 5: The student will solve constructed response items such as
this:
Point S is located at (-5,7) and point T is located at (-1,-1).
a. Graph the segment.
b. Find the length of segment ST. (
)
c. Find the coordinates of R such that R divides segment ST into a ratio of 1:3.
(R(-4,5))
d. Verify that the ratio of SR:RT is 1:3 using the distance formula.
e. Find the equation of the line perpendicular to segment ST that passes through
1
R and graph the line. ( y  x  7 )
2
GeometryUnit 3Parallel and Perpendicular Relationships
3-13