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Lesson 1
7-2 Parallel and Perpendicular Lines
J. Frazier
Standard(s) M8G1 Students will understand and apply the properties of parallel and perpendicular lines and
understand the meaning of congruence.
Elements:
a. Investigate characteristics of parallel and perpendicular lines both algebraically and geometrically.
b. Apply properties of angle pairs formed by parallel lines cut by a transversal.
M8A1 Students will use algebra to represent, analyze, and solve problems.
Elements:
a. Represent a given situation using algebraic expressions or equations in one variable.
c. Solve algebraic equations in one variable, including equations involving absolute values.
Stage 
DESIRED RESULTS
Understandings
Method Focus for Teaching Gifted: Inquiry/Discovery Method; Creative Problem Solving
Essential Questions
Knowledge & Skill
 How do you determine whether a line is
Students will be able to…
parallel or perpendicular?
-distinguish between parallel and perpendicular lines.
 What types of angles are formed when two
-identify the right angles formed by perpendicular
parallel lines are cut by a transversal?
lines.
-construct parallel lines cut by a transversal and
identify alternate interior angles, alternate exterior
angles, vertical angles, and corresponding angles.
-use such angles to determine the angle measures.
Stage 
ASSESSMENT EVIDENCE
 Three labeled diagrams of lines found in
 Modification for gifted: Self-assess, peer
school or created by student with rubric for
assess, teacher assess with modified rubric
assessment
Stage 
LEARNING ACTIVITIES
-Opening: Review meaning of parallel and perpendicular lines, transversal. Discuss real life examples of these.
-Sketch parallel and perpendicular lines into notebook. In pairs, brainstorm places that both may be found.
-Use information of pages 330-332 to review complementary and supplementary angles and pull all of gathered
information together. Discuss examples in book.
-Scour the school for examples of perpendicular lines and parallel lines cut by a transversal. Sketch and bring
back to class. Use sketches, colored pencils, and diagrams of angle types to identify types of angles.
-Modification for gifted: While class uses diagrams to identify angles, gifted students construct a diagram of a
room showing each type of angle used in the creation of such.
Lesson vocabulary: parallel lines, perpendicular lines, transversal, alternate interior angles, alternate exterior
angles, vertical angles, corresponding angles, supplementary, complementary, right angle
Lesson 2
7-3 Angles in Triangles
J. Frazier
Standard(s) M8G1 Students will understand and apply the properties of parallel and perpendicular lines and
understand the meaning of congruence.
Elements:
b. Apply properties of angle pairs formed by parallel lines cut by a transversal.
M8A1 Students will use algebra to represent, analyze, and solve problems.
Elements:
a. Represent a given situation using algebraic expressions or equations in one variable.
c. Solve algebraic equations in one variable, including equations involving absolute values.
d. Solve equations involving several variables for one variable in terms of the others.
Stage 
DESIRED RESULTS
Understandings
Method Focus for Teaching Gifted: Inquiry/ Discovery Method
Essential Questions
Knowledge & Skill
 What is the sum of angles of a triangle?
Students will be able to…
 How is the measure of a missing angle
-state the sum of angle measures in a triangle.
measure found?
-calculate the measure of missing angle measures of a
triangle.
Stage 
 Teacher observation
 Quiz
ASSESSMENT EVIDENCE
 Modified assessment for gifted: Have students
create a quiz with 10 questions and an answer
key using the class quiz as a model on the
computer. Print out and turn in to teacher.
Stage 
LEARNING ACTIVITIES
-Opening: Use a rubber band to form a triangle with different measures. Show students that if one of the angles
gets larger, another angle gets smaller.
-Give each student a paper triangle. Have them tear off two corners and place corners together next to the third
angle to see that they for a straight line.
-Discuss examples and guided practice on pages 336-338.
Lesson vocabulary: Triangle Sum Theorem, acute triangle, right triangle, obtuse triangle, equilateral triangle,
isosceles triangle, scalene triangle
Lesson 3
7-4 Classifying Polygons
J. Frazier
Standard(s) M8A1 Students will use algebra to represent, analyze, and solve problems.
Elements:
a. Represent a given situation using algebraic expressions or equations in one variable.
M8G1 Students will understand and apply the properties of parallel and perpendicular lines and understand the
meaning of congruence.
Elements:
d. Understand the meaning of congruence: that all corresponding angles are congruent and all corresponding
sides are congruent.
Stage 
DESIRED RESULTS
Understandings
Method Focus for Teaching Gifted: Technology
Essential Questions
Knowledge & Skill
 What criteria are needed to classify a polygon? Students will be able to…
 How is the total of angle measures in a given
-classify various types of polygons
polygon calculated/ represented?
-determine the individual and total of angle measures
in various regular and irregular polygons
Stage 
ASSESSMENT EVIDENCE
 Teacher observation of participation in
 Modification for gifted: modified rubric
discussions
 Graded practice
 Rubric for powerpoint
Stage 
LEARNING ACTIVITIES
-Opening: Show students the prefixes: tri-, quad-, penta-, hexa-, hepta-, and octa-. Ask them to think of words
that begin with these prefixes, such as tricycle, quadruple, and octopus. Discuss vocabulary terms.
-Discuss examples in book on pages 341 and 342.
-Brainstorm places each type of polygon could be found in real life and their significance there.
-Practice sheet 7-4B
-Have students work in pairs to make a powerpoint describing each vocabulary term and showing an example.
-Modification for gifted: Have students search the internet for places in real life that each type of polygon may
be found. Include examples for each in their powerpoint.
Lesson vocabulary: polygon, regular polygon, trapezoid, parallelogram, rectangle, rhombus, square, triangle,
quadrilateral, pentagon, hexagon, heptagon, octagon
Lesson 4
7-5 Coordinate Geometry
J. Frazier
Standard(s) M8G1 Students will understand and apply the properties of parallel and perpendicular lines and
understand the meaning of congruence.
Elements:
a. Investigate characteristics of parallel and perpendicular lines both algebraically and geometrically.
M8A4. Students will graph and analyze graphs of linear equations and inequalitites.
Elements:
a. Interpret slope as a rate of change.
M8P4. Students will make connections among mathematical ideas and to other
disciplines.
Elements:
a. Recognize and use connections among mathematical ideas.
b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
Stage 
DESIRED RESULTS
Understandings
Method Focus for Teaching Gifted: Questioning
Essential Questions
Knowledge & Skill
 How do you determine if two parallel lines are Students will be able to…
truly parallel or perpendicular?
-determine slope of a graphed line.
 How does slope help us to compare lines?
-compare two lines using their slopes.
Stage 
ASSESSMENT EVIDENCE
 Teacher observation
 Ticket out the door: Explain how two lines
that appear to be parallel may not actually be
so.
Stage 
LEARNING ACTIVITIES
-Opening: Show students two lines that appear to be parallel and ask them if they really are. Suggest that
although they appear to be parallel, the appearance is not proof.
-Use q & a about previously learned information on slope to help students realize that lines may meet in some
far off place/ slope can be used to determine if they are truly parallel or perpendicular
-Use q & a to help students discover that slope can be found on a graphed line by determining rise over run.
-Guided practice on page 348, 349
-Modification for gifted: Give students questions and allow them as a group to explore the questions and come
up with a hypothesis as to how lines can be determined to be parallel or perpendicular.
Lesson vocabulary: slope, rise, run, horizontal line, vertical line
Lesson 5
7-6 Congruence
J. Frazier
Standard(s) M8G1. Students will understand and apply the properties of parallel and perpendicular lines and
understand the meaning of congruence.
Elements:
d. Understand the meaning of congruence: that all corresponding angles are congruent and all corresponding
sides are congruent.
M8A1. Students will use algebra to represent, analyze, and solve problems.
Elements:
a. Represent a given situation using algebraic expressions or equations in one variable.
c. Solve algebraic equations in one variable, including equations involving absolute values.
Stage 
DESIRED RESULTS
Understandings
Method Focus for Teaching Gifted: Use of Questions/ Technology
Essential Questions
Knowledge & Skill
 How do you determine whether an angle or
Students will be able to…
side is congruent to another angle or side?
-compare two congruent figures.
 What factors are used to determine whether or -identify corresponding sides and angles in congruent
not two figures are congruent?
figures.
Stage 
 Graded practice
ASSESSMENT EVIDENCE
 Modification for gifted: Have students use the
computer to create a “hidden shapes” picture
with at least five sets of congruent figures.
Graded with rubric.
Stage 
LEARNING ACTIVITIES
-Opening: Show the students two triangles that are congruent. Ask them what they notice about the triangles.
Allow students to respond with answers such as “they have the same size and shape,” “the sides are the same
length,” and “the angles have the same measure.”
-Use q & a to guide students through the definition of correspond, corresponding sides, and corresponding
angles. Place one triangle on top of the other to show that one completely covers the other.
-Discuss book examples and practice several problems together, identifying corresponding parts and
determining if the figures are congruent.
-Have students practice independently (see gifted mod. above.)
Lesson vocabulary: correspondence, corresponding angles, corresponding sides, congruent