Lesson 9 Symmetry in Action

    • Let’s investigate symmetry and perimeter in folded figures.

Warm-up Which One Doesn’t Belong: Figures

Which one doesn’t belong?

  1. quadrilateral with two right angles
  2. a kite shaped figure with a top right angle marked
  3. front of a cylinder
  4. diagram with two right angles and four unmarked angles

Activity 1 Before and After

  1. Mai has a piece of paper. She can get two different shapes by folding the paper along a line of symmetry. What is the shape of the paper before it was folded?

    right triangle and rectangle

  2. Diego folded a piece of paper once along a line of symmetry and got this right triangle.

    right triangle

    Which shapes could the paper have before it was folded? Explain or show how you know.

    triangle A. parallelogram B.
    rectangle C. triangle D.
    parallellogram E. trapezoid F.

Activity 2 Before and After, Perimeter Edition

Problem 1

Jada folded a piece of paper along a line of symmetry and got this rectangle.

rectangle with sides labeled 105 mm and 182 mm

  1. What could the paper look like before being folded? Draw one or more sketches.

  2. Write an expression for the perimeter of the unfolded paper.

Problem 2

Kiran folded a piece of paper twice—each time along a line of symmetry—and got the same rectangle as Jada did.

Show that each expression could represent the perimeter of the paper Kiran folded.

Practice Problem

Problem 1

Here is a rectangle R.

  1. What shape can be folded along a line of symmetry to give R? What are the side lengths of that shape?

    rectangle with one side 15 cm and one side 21 cm.

  2. What shape can be folded twice along lines of symmetry to give R? What are its side lengths?