Lesson Title: ___Angles and Triangles___________________________ Course: ___________CC8____________
Date: _____________ Teacher(s): ____________________
Start/end times: _________________________
Lesson Standards/Objective(s): What mathematical skill(s) and understanding(s) will be developed? Which
Mathematical Practices do you expect students to engage in during the lesson?
8.G.A.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles,
about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for
similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three
angles appears to form a line, and give an argument in terms of transversals why this is so.
MP1:
MP3:
MP5:
MP7:
MP8:
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Use appropriate tools strategically.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Lesson Launch Notes: Exactly how will you use the
first five minutes of the lesson?
What does parallel mean?
Sample answer: Two (or more) lines, segments, or rays
that are in the same plane and never intersect; they are
always the same distance apart.
List everything you already know about triangles.
Sample Answers: They have 3 sides. They have 3
angles. They can be right, obtuse, or acute. They can
be scalene, isosceles, or equilateral.
Lesson Closure Notes: Exactly what summary activity,
questions, and discussion will close the lesson and
connect big ideas? List the questions. Provide a
foreshadowing of tomorrow.
Each day, have students write a list of the Big Ideas they
got from the day’s activities, and think-pair-share.
Distribute the Culminating Activity after the entire lesson
is finished.
Lesson Tasks, Problems, and Activities (attach resource sheets): What specific activities, investigations,
problems, questions, or tasks will students be working on during the lesson? Be sure to indicate strategic
connections to appropriate mathematical practices.
Note: This lesson spans multiple class periods.
Interior Angles of a Triangle
1. Ask students what the word interior means to them. Likely answers will include the idea of inside. Interior
decorating is decorating the inside of a house, for example.
2. Distribute the Triangle Shapes resource sheet. Ask students to place their finger where they believe an interior
angle of one of the triangles is located. Circulate to verify that they are in the correct place, then define interior
angles.
3. Distribute Triangle Shapes Exploration 1: Interior Angles, and Patty Paper. Have rulers and protractors
available for student use as well.
4. Be sure that the students understand the directions, then circulate as they complete the exploration. (Look for
evidence of MP1, MP5.)
5. Allow students to share their observations. (Look for evidence of MP3, MP7, and MP8.)
6. Make sure that the following points are brought out in the discussion:
a. The three angles form a straight line when arranged with their vertices overlapping and where two
angles share a common side.
b. The sum of the interior angles of a triangle is always 180 degrees.
7. Extend by having students use protractors to verify the angle measurements, if they have not done so already.
HCPSS Secondary Mathematics Office (v2.1); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: ___Angles and Triangles___________________________ Course: ___________CC8____________
Date: _____________ Teacher(s): ____________________
Start/end times: _________________________
Exterior Angles of a Triangle
1. Ask students what the word exterior means to them. Likely answers will include the idea of outside. You may
show them a can of exterior house paint and discuss how it differs from interior house paint.
2. Refer students back to the Triangle Shapes resource sheet.
3. Distribute Triangle Shapes Exploration 2: Exterior Angles, and Patty Paper. Have rulers and protractors
available for student use as well.
4. Be sure that the students understand the directions (especially how to draw the exterior angles), then circulate as
they complete the exploration. (Look for evidence of MP1, MP5.)
5. Allow students to share their observations. (Look for evidence of MP3, MP7, and MP8.)
6. Make sure that the following points are brought out in the discussion:
a. The three angles form a complete circle when arranged with their vertices overlapping and where two
angles side.
b. The sum of the interior angles of a triangle is always 360 degrees.
7. Extend by having students use protractors to verify the angle measurements, if they have not done so already.
Note: You may wish to have the students draw the exterior angles of one of the triangles by going in the opposite
direction and verify that the angles still add to 360.
Similar Triangles
1. Ask students what the word similar means to them, and ask for examples. Likely answers will include the idea
that things are basically the same with just one or two differences. Shoes that come in different sizes are similar
to one another because they have the same shape, same logo, same number of holes for laces, but the size of each
shoe is different.
2. Introduce the vocabulary for similar triangles (or polygons), and emphasize that similar figure have the same
shape but a different size. Do not discuss specifics yet.
3. Distribute the Similar Triangles resource sheet.
4. Distribute Similar Triangles Exploration, and Patty Paper. Have rulers and protractors available for student use
as well.
5. Be sure that the students understand the directions, then circulate as they complete the exploration. (Look for
evidence of MP1, MP5.)
6. Allow students to share their observations. (Look for evidence of MP3, MP7, and MP8.)
7. Make sure that the following points are brought out in the discussion:
a. Similar triangles have corresponding angles that are congruent.
b. Two sets of corresponding, congruent angles are necessary to show that two triangles are similar.
8. Extend by having students use protractors to verify the angle measurements, if they have not done so already.
Parallel Lines
1. Recall the definition of parallel lines given during the Lesson Launch.
2. Introduce vocabulary for transversal, and the idea that a transversal is a line that intersects two or more other
lines.
3. Show the students several examples of lines (parallel and not parallel), and have them identify the transversal.
Include an example, as shown below, and make sure the students understand that a transversal is relative to the
other lines being discussed.
w is a transversal of lines y and z
y is a transversal of lines w and x
HCPSS Secondary Mathematics Office (v2.1); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: ___Angles and Triangles___________________________ Course: ___________CC8____________
Date: _____________ Teacher(s): ____________________
Start/end times: _________________________
y
z
w
x
4. Distribute the Parallel Lines resource sheet.
5. Distribute Parallel Lines Exploration, and Patty Paper. Have rulers and protractors available for student use as
well.
6. Be sure that the students understand the directions, then circulate as they complete the exploration. (Look for
evidence of MP1, MP5.)
7. Have students share their observations. (Look for evidence of MP3, MP7, and MP8.)
8. Make sure that the following points are emphasized in the discussion:
a. All of the acute angles are congruent.
b. All of the obtuse angles are congruent.
c. An acute angle plus an acute angle form a linear pair (180 degrees).
9. Formalize the vocabulary for alternate interior angles, alternate exterior angles, vertical angles, same side
interior angles, and same side exterior angles. Remind students of the definition of corresponding angles.
10. Have the students refer to the Parallel Lines Student Resource sheet, and ask them to identify each of the pairs
of angles. Emphasize the relative nature of the terms, e.g. Angle 1 and Angle 6 are a pair of alternate exterior
angles, but Angle 1 and Angle 8 are corresponding angles. Angles have different relationships based on which
angle it is being compared to, just as deciding whether a line is a transversal depends on which other lines you
are interested in.
Note: If students are having difficulty with this topic, choose a student and explain that he or she may be a
brother or sister to their sibling, but they are a son or daughter to a parent.
Culminating Activity
1. Distribute the Culminating Activity.
2. Explain that because the Sun is so large in comparison to the Earth, and the distance between them is so great,
they can assume that the rays of the sun that are hitting the Earth are parallel to one another.
3. Have students complete the activity alone or in pairs.
Note: You may choose to have students share their answers before collecting and checking the activity.
Evidence of Success: What exactly do I expect students to be able to do by the end of the lesson, and how will I
measure student success? That is, deliberate consideration of what performances will convince you (and any outside
observer) that your students have developed a deepened and conceptual understanding.
Students will understand that the sum of the interior angles of a triangle is 180 degrees.
Students will understand that the sum of the exterior angles of a triangle is 360 degrees.
Students will understand that similar triangles have corresponding angles that are congruent.
Students will understand that 2 pairs of congruent, corresponding angles is enough to determine that two triangles
are similar.
Students will be able to label the angle pairs formed when two parallel lines are cut by a transversal and identify
congruent and supplementary pairs.
HCPSS Secondary Mathematics Office (v2.1); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: ___Angles and Triangles___________________________ Course: ___________CC8____________
Date: _____________ Teacher(s): ____________________
Start/end times: _________________________
Students will be able to complete the Culminating Activity successfully, using appropriate vocabulary.
Notes and Nuances: Vocabulary, connections, anticipated misconceptions (and how they will be addressed), etc.
This lesson will span multiple (3-5) days. The activities will help to guide discussion.
Vocabulary: Interior Angle, Exterior Angle, Corresponding Angles, Transversal, Alternate Interior Angles,
Alternate Exterior Angles
Resources: What materials or resources are essential
for students to successfully complete the lesson tasks or
activities?
Homework: Exactly what follow-up homework tasks,
problems, and/or exercises will be assigned upon the
completion of the lesson?
8.6.A.5 Student Resource
Patty Paper
Protractors
Rulers
8.6.A.5 Culminating Activity
To be determined by teacher
Lesson Reflections: How do you know that you were effective? What questions, connected to the lesson
standards/objectives and evidence of success, will you use to reflect on the effectiveness of this lesson?
Were students engaged in the tasks?
Were the students able to construct viable arguments and critique the reasoning of others during the discussions?
Were the students able to successfully complete the culminating activity?
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this
product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.
HCPSS Secondary Mathematics Office (v2.1); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.