Parallelograms
5 min
Teacher Prep
Setup
Narrative
In this activity, students examine examples and non-examples of parallelograms and identify their defining characteristics. Students recall that a parallelogram is a quadrilateral whose opposite sides are parallel. They observe other properties that follow from that definition—that opposite sides of a parallelogram have the same length and opposite angles have the same measure.
Launch
Display the images of Figures A–F for all to see. Tell students that Figures A, B, and C are parallelograms and Figures D, E, and F are not parallelograms.
Arrange students into groups of 2 and provide access to geometry toolkits. Give students 1–2 minutes of quiet think time to complete the task. Afterward, give them a minute to discuss their answers and observations with their partner.
Student Task
Figures A, B, and C are parallelograms.
Figures D, E, and F are not parallelograms.
What do you notice about:
- The number of sides that a parallelogram has?
- Opposite sides of a parallelogram?
- Opposite angles of a parallelogram?
Sample Response
- Parallelograms have four sides.
- Opposite sides of parallelograms are parallel and have the same length.
- Opposite angles of parallelograms have the same measure.
Activity Synthesis (Teacher Notes)
Ask a few students to share their responses to the questions. After each response, ask students to indicate whether they agree. If a student disagrees, discuss the disagreement. Record the agreed-upon responses for all to see and highlight these characteristics of parallelograms:
- A parallelogram is a quadrilateral (a polygon with four sides).
- Both pairs of its opposite sides are parallel.
- Its opposite sides have the same length.
- Its opposite angles have the same measure.
Students may wonder how to know if two non-horizontal or non-vertical sides of a figure are parallel. Explain that because parallel lines never intersect, the length of any perpendicular line segments between them are the same length. Consider demonstrating how to use an index card to check this in Figures A and C.
Tell students that for now we will just take these characteristics of parallelograms as facts. Later they will learn some ways to prove that these characteristics are always true.
Anticipated Misconceptions
Students may not realize that Figure C is a square or relate Figure C to the other parallelograms because of its orientation. Encourage students to use patty paper or another tool in the geometry toolkit to help them compare the characteristics of Figure C to those of Figures A and B.
Standards
- 4.G.2·Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. (Two-dimensional shapes should include special triangles, e.g., equilateral, isosceles, scalene, and special quadrilaterals, e.g., rhombus, square, rectangle, parallelogram, trapezoid.)
- 4.G.A.2·Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.
- 5.G.B·Classify two-dimensional figures into categories based on their properties.
- 5.G.B·Classify two-dimensional figures into categories based on their properties.
15 min
15 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Parallelograms
5 min
Teacher Prep
Setup
Narrative
In this activity, students examine examples and non-examples of parallelograms and identify their defining characteristics. Students recall that a parallelogram is a quadrilateral whose opposite sides are parallel. They observe other properties that follow from that definition—that opposite sides of a parallelogram have the same length and opposite angles have the same measure.
Launch
Display the images of Figures A–F for all to see. Tell students that Figures A, B, and C are parallelograms and Figures D, E, and F are not parallelograms.
Arrange students into groups of 2 and provide access to geometry toolkits. Give students 1–2 minutes of quiet think time to complete the task. Afterward, give them a minute to discuss their answers and observations with their partner.
Student Task
Figures A, B, and C are parallelograms.
Figures D, E, and F are not parallelograms.
What do you notice about:
- The number of sides that a parallelogram has?
- Opposite sides of a parallelogram?
- Opposite angles of a parallelogram?
Sample Response
- Parallelograms have four sides.
- Opposite sides of parallelograms are parallel and have the same length.
- Opposite angles of parallelograms have the same measure.
Activity Synthesis (Teacher Notes)
Ask a few students to share their responses to the questions. After each response, ask students to indicate whether they agree. If a student disagrees, discuss the disagreement. Record the agreed-upon responses for all to see and highlight these characteristics of parallelograms:
- A parallelogram is a quadrilateral (a polygon with four sides).
- Both pairs of its opposite sides are parallel.
- Its opposite sides have the same length.
- Its opposite angles have the same measure.
Students may wonder how to know if two non-horizontal or non-vertical sides of a figure are parallel. Explain that because parallel lines never intersect, the length of any perpendicular line segments between them are the same length. Consider demonstrating how to use an index card to check this in Figures A and C.
Tell students that for now we will just take these characteristics of parallelograms as facts. Later they will learn some ways to prove that these characteristics are always true.
Anticipated Misconceptions
Students may not realize that Figure C is a square or relate Figure C to the other parallelograms because of its orientation. Encourage students to use patty paper or another tool in the geometry toolkit to help them compare the characteristics of Figure C to those of Figures A and B.
Standards
- 4.G.2·Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. (Two-dimensional shapes should include special triangles, e.g., equilateral, isosceles, scalene, and special quadrilaterals, e.g., rhombus, square, rectangle, parallelogram, trapezoid.)
- 4.G.A.2·Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.
- 5.G.B·Classify two-dimensional figures into categories based on their properties.
- 5.G.B·Classify two-dimensional figures into categories based on their properties.