Lesson 5
Trapezoids
Warmup: What Do You Know About Trapezoids? (10 minutes)
Narrative
Launch
 “What do you know about trapezoids?”
 1 minute: quiet think time
Activity
 Record responses.
Student Facing
Student Response
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Activity Synthesis
 “Draw some examples of trapezoids.”
 Invite a few students to share their trapezoids with the rest of the class.
 “How do you know these are trapezoids?” (They have one pair of parallel sides or they have at least one pair of parallel sides.)
Activity 1: What’s a Trapezoid? (20 minutes)
Narrative
Launch
 Display:
 “Some parallelograms are rectangles.”
 “All parallelograms are squares.”
 “Is each statement true or false?” (I think that a parallelogram can be a rectangle but it does not have to be a square.)
 1 minute: partner discussion
Activity
 Groups of 2
 5 minutes: independent work time
 5 minutes: partner work time
 Monitor for students who:
 draw an isosceles trapezoid
 draw a nonisosceles trapezoid
Student Facing

Draw a trapezoid. Label the coordinates of the grid points you used.
 Is it a square? Rectangle? Rhombus? Parallelogram? Explain your reasoning.
 Describe a trapezoid in your own words. Compare your definition with a partner.

Is this shape a trapezoid according to your definition? Explain your reasoning.
Student Response
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Advancing Student Thinking
Activity Synthesis
 Display: isosceles trapezoid and nonisosceles trapezoid from student solution or use student work
 “How are these two shapes the same? How are they different?” (They both have a pair of parallel sides. One has a pair of equal sides. The other one does not.)
 Display parallelogram from the last problem in student workbook and this text:
“A trapezoid . . .”
“. . . has exactly one pair of opposite sides parallel.”
“. . . has at least one pair of opposite sides parallel.”
 “According to which definition is this shape a trapezoid? Why?” (the second definition because it has 2 pairs of parallel sides)
 “We’ll continue to explore these two definitions further in the next activity.”
Activity 2: Two Definitions of a Trapezoid (15 minutes)
Narrative
The purpose of this activity is to further explore the two definitions of trapezoids and the hierarchy of quadrilaterals. Students evaluate different statements relating trapezoids and parallelograms deciding whether they are true or false with each definition. The activity synthesis establishes the convention for these materials that a trapezoid is a quadrilateral with at least one pair of parallel sides. As students discuss and justify their decisions, they reason clearly using the 2 definitions of trapezoid (MP6).
Advances: Reading, Representing
Supports accessibility for: Conceptual Processing; Language
Launch
 Groups of 2.
 Display 2 Venn diagrams for parallelograms and trapezoids.
 “What do you notice? What do you wonder?” (One diagram shows parallelograms are part of trapezoids and the other one shows there is no overlap.)
 1 minute: partner discussion
Activity
 5 minutes: independent work time
 5 minutes: partner work time
 Monitor for students who:
 can articulate the differences between the two definitions
 draw examples of shapes to help evaluate each statement
 accurately explain the difference between the two definitions
Student Facing
Definition 1
Definition 2
A trapezoid has exactly one pair of opposite sides that are parallel.
A trapezoid has at least one pair of opposite sides that are parallel.
Which statements go with the first definition? Which statements go with the second definition? Explain or show your reasoning.
 All parallelograms are trapezoids.
 No parallelograms are trapezoids.
 All trapezoids are parallelograms.
 Some trapezoids are parallelograms.
 No trapezoids are parallelograms.
Student Response
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Advancing Student Thinking
If students do not sort the statements correctly, suggest they sort the shape cards from an earlier lesson according to the two definitions. Then show them one statement at a time and ask, “Is this statement true of all the shapes in one of these groups?”
Activity Synthesis
 Invite previously selected students to share.
 “Some people use the first definition of the trapezoid. We will be using the second definition.”
 Display Venn diagrams from student workbook.
 “What does each diagram mean?” (Definition 2 shows that a parallelogram is a trapezoid but a trapezoid doesn’t have to be a parallelogram. Definition 1 shows that trapezoids and parallelograms are distinct: a parallelogram can't be a trapezoid and a trapezoid can't be a parallelogram.)
 “Which diagram matches the definition of trapezoid we will use?” (The one on the right, Definition 2, because if a shape is a parallelogram it is also a trapezoid, but if a shape is a trapezoid, it doesn’t have to be a parallelogram.)
 Consider asking students to draw:
 A trapezoid that is also a parallelogram.
 A trapezoid that is not a parallelogram.
Lesson Synthesis
Lesson Synthesis
“Today we looked at 2 different definitions for a trapezoid.”
“What do you know about trapezoids now?” (A trapezoid is a quadrilateral and has at least one pair of parallel sides. If a shape is a parallelogram, it is also a trapezoid.)
Draw or display shapes like these:
“Which of these shapes are trapezoids? How do you know?” (B, C, and D are trapezoids because they each have at least one pair of parallel sides.)
Display or draw a Venn diagram like the one below. Save the diagram to refer back to it in future lessons.
“Where would these shapes go in the diagram?”
Draw the shapes as students share.
Cooldown: Which Ones are Trapezoids? (5 minutes)
CoolDown
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