Angles and Lines Lesson Plan
Objectives:
 Students will be able to define plane, parallel, perpendicular, intersecting
congruent, vertical angles, corresponding angles, supplementary angles and
adjacent angles
 Students will be able to determine the difference between vertical, corresponding,
supplementary and adjacent angles
 Students will be able to apply these definitions to solve real world problems
Maryland State Standards:
 The student will analyze properties of geometric figures
o Congruence and similarity
o Line/segment/plane relationships (parallel, perpendicular, intersecting,
bisecting, midpoint, median, altitude)
o Angles and Angle relationships (vertical, adjacent complementary,
supplementary, obtuse, acute, right, interior, exterior)
National Standards:
 represent, analyze, and generalize a variety of patterns with tables, graphs, words,
and, when possible, symbolic rules;
 relate and compare different forms of representation for a relationship
 explore relationships between symbolic expressions and graphs of lines, paying
particular attention to the meaning of intercept and slope;
 use symbolic algebra to represent situations and to solve problems, especially
those that involve linear relationships
Warm Up:
Students will be given the attached worksheet that has two diagrams of
intersecting lines. The worksheet also has a diagram of two parallel lines cut by a
transversal to indicate corresponding angles. For the exploration activity students will be
given these worksheets along with scissors.
Homework Check: The homework solutions will be presented and students will have
time to ask any questions they had on the homework problems.
Exploration/Explanation
Students will be given the attached worksheet that has two diagrams of
intersecting lines. The worksheet also has a diagram of two parallel lines cut by a
transversal to indicate corresponding angles. For the exploration activity students will be
given these worksheets along with scissors.
Also, the students will be given a matching worksheet that has all of the new
vocabulary words for this chapter along with their definitions. As we work through the
cutting activity I will draw the student’s attention to the matching and they will find the
correct definition for each word as we discuss each new vocabulary word. The first
diagram is illustrated below:
Cut along this line
1
4
2
3
From this diagram students will take their scissors
and be instructed to cut along the line so that they will have two separate sheets of paper
one with the supplementary angles of 1 and 4 and one with the supplementary angles of 2
and 3. Then the students will be instructed to stop cutting. From yesterday the students
have already learned about supplementary angles. I will ask the students what type of
angles 1 and 4 are and 2 and 3.
Expected Student Response: Supplementary angles because their sum adds up to
180 degrees.
I will then move on to the first new vocabulary word adjacent angles.
I will hold my two cut outs up and ask the class that we know these angles are
supplementary because they add up to 180 degrees. But what do you think I mean if I
told you these angles are adjacent as well.
Expected Student Response: They are next to each other.
I will then ask the students to look at their matching worksheet to see if they can
match up the vocabulary word adjacent with its proper definition. I will ask them to look
for cues in the definition that would mean an angle is next, or side by side, to another
angle.
Before we move onto the next vocabulary words I will instruct the students
attention back to the worksheet they began to cut up. On the bottom there is the same
diagram from above with the question “Name all pairs of adjacent, supplementary
angles:” We will work this as a class to fill in the four blanks before we move on to the
next vocabulary word.
Name all the pairs of adjacent, supplementary angles:
1 and 2
2 and 3
3 and 4
4 and 1
1
4
2
3
Identify the pairs of congruent, vertical angles:
1 and 3
2 and 4
This will lead directly into the next vocabulary word of vertical angles. I will cue
the students by saying if we just said that angles 1 and 4 and 2 and 3 are adjacent then
what can we say about 2 and 4, and angles 1 and 3?
Expected Student Response: They are opposite of one another.
I will tell the students that these angles that are opposite one another are called
vertical angles. Once, I have told the students this they will again go and match the
proper definition to the vocabulary word. They will refer back to the diagram above and
we will fill in the pairs of congruent, vertical angles.
I will then instruct the students to cut along second line of their diagrams giving
them the four separate angles 1, 2, 3 and 4. I will then ask the students to place angles 1
and 3 on top of one another and angles 2 and 4 on top of one another. I will ask the class
what they notice about the angles.
Expected Student Response: The angles are the same.
I will explain to the students that when two angles are the same we call them
congruent angles. I will then again instruct the students to match the vocabulary word
with it’s proper definition.
Now the students will be instructed to put their scissors and paper down and I will
explain the vocabulary word plane to the students. I will give them the definition that a
plane is a flat surface that does not end. I will then give them several examples such as
the xy-plane and the floor of the classroom. I will then ask a few students to look around
the classroom and give me another example of a plane that they see.
Expected Student Response: The wall, the blackboard and our desks.
Once I feel the students have grasped this slightly more abstract concept of plane I
will move on to the vocabulary words of intersecting, parallel and perpendicular lines.
I will ask the students what does it mean when two lines intersect?
Expected Students Response: The two lines will cross.
I will then ask what do they create when they cross?
Expected Student Response: A point.
Then I will ask if anyone knows what parallel lines are and what perpendicular
lines are. I will wait for students to raise their hand to answer. If students answer then I
will use their answers to get them to the correct definition of parallel and perpendicular
lines. If no students raise their hands I will explain that parallel lines are lines that are in
the same plane that do not intersect and I will provide an example. Then I will explain
perpendicular lines are lines that intersect to form four right angles and I will also give
them an example. The students will be instructed to match intersecting, parallel and
perpendicular lines with their proper definitions.
Finally, I will get to the second diagram of corresponding angles. I will provide
the students with the definition and following example of corresponding angles:
1
2
I will then ask the students why do these
angles correspond?
Expected Student Response: Because they are in the same position in relation to
the line cutting through.
The students will then get their scissors and cut out the final pieces to illustrate
congruent corresponding angles only if the two lines are parallel. They will cut out along
the dotted line of the following two diagrams:
1
3
2
4
Once they have cut along the dotted line they will be instructed to place their two pieces
on top of one another. Then they will be instructed to hold these pieces up to the light. I
will ask them what they notice about angles 1 and 2 of the first diagram?
Expected Student Response: They are not the same because the lines are not
parallel.
Then I will ask them what they notice about the second two angles 3 and 4?
Expected Student Response: They are the same because the two lines are
parallel thus creating congruent corresponding angles.
Extension
Once we have completed the matching and cutting activities above the students
will be given a worksheet for their independent work. They will use the diagram in this
work sheet to label the special types of angle names. They will be given a word bank and
need to use the words in the word bank to complete the missing words of the sentences.
After the students work on their independent worksheet will come together and go over
their answers as a class. I will ask the students what they got for each sentence and have
them explain why they choose that as their answer so I can check for their understanding.
The worksheet is attached below.
A
1
2
4
Redskins Road
Orioles Blvd.
3
Capitals Drive
Wizards
Way
5
Ravens Lane
6
7
8
Word Bank
Plane
Parallel
Vertical
Corresponding
Perpendicular
Intersecting
Supplementary
Congruent – 2
Adjacent
1 and
4 are ______________ angles and _______________ angles.
3 and
4 are ______________ angles and these angles are the same, also known as
_______________.
2 and
6 are ______________ angles and because Capitals Drive
is ______________ to Ravens Lane they are also _______________ angles. Wizards
Way and Ravens Lane are an example of _____________ lines. Orioles Blvd. and
Ravens Lane are a unique example of interesting lines that create four right angles known
as ________________ lines. Finally, the Letter A at the top of the diagram above refers
to the flat surface these streets lay in called a ________________.
Extension Problem
Using the diagram above answer the following questions: If the 5 = 80∘ then what is
the measure of 7?__________. What is the measure of 1?___________. What is the
measure of 6?____________. What is the measure of 3?___________.
A
1
2
4
Redskins Road
Orioles Blvd.
3
Capitals Drive
Wizards
Way
5
Ravens Lane
6
7
8
Word Bank
Plane
Parallel
Vertical
Corresponding
1 and
Perpendicular
Congruent – 2
Intersecting
Supplementary
4 are Vertical angles and Congruent angles.
Adjacent
3 and
4 are Supplementary
angles and these angles share a common so side they are also known as Adjacent.
and
2
6 are Corresponding angles and because Capitals Drive is Parallel to Ravens Lane
they are also Congruent angles. Wizards Way and Ravens Lane are an example of
Intersecting lines. Orioles Blvd. and Ravens Lane are a unique example of interesting
lines that create four right angles known as Perpendicular lines. Finally, the Letter A at
the top of the diagram above refers to the flat surface these streets lay in called a Plane.
Extension Problem
Using the diagram above answer the following questions: If the
the measure of
8 80∘. What is the measure of
100∘. What is the measure of
3? 100∘
5 = 80∘ then what is
7? 100∘. What is the measure of
6?
1
4
2
3
1
3
2
4
Name all the pairs of adjacent, supplementary angles:
____________
_____________
____________
_____________
1
4
2
3
Identify the pairs of congruent, vertical angles:
____________
_____________
Matching Vocabulary
____ Adjacent Angles
1. A flat surface that extends without end
____ Vertical Angles
2. Two lines in the same plane that do not
intersect
____ Congruent Angles
____ Plane
3. Angles that occupy corresponding positions
when a line interests two other lines
____ Parallel Lines
4. Two lines intersect to form four right angles
____ Intersecting Lines
5. Two lines that meet at a point
____ Perpendicular Lines
6. Two angles that share a common side and a
vertex and do not overlap
____ Corresponding Angles
7. Two angles that have the same measure
8. Angles opposite each other
Matching Vocabulary
6
Adjacent Angles
9. A flat surface that extends without end
8
Vertical Angles
10. Two lines in the same plane that do not
intersect
7
Congruent Angles
1
Plane
11. Angles that occupy corresponding positions
when a line interests two other lines
2
Parallel Lines
12. Two lines intersect to form four right angles
5
Intersecting Lines
13. Two lines that meet at a point
4
Perpendicular Lines
3
Corresponding Angles
14. Two angles that share a common side and a
vertex and do not overlap
15. Two angles that have the same measure
16. Angles opposite each other