Section B: Practice Problems Reason about Attributes to Solve Problems

Section Summary


In this section, we used the attributes such as side lengths, angles, lines of symmetry, and parallel sides to solve problems about perimeter of shapes.

We learned that, if a shape has certain attributes, we can use them to find its perimeter, even if we don’t have all of its side lengths. Or, if we know the perimeter of a shape, we can find its side lengths if there is enough information about their attributes.

For example, here are two shapes:

pentagon A with a line of symmetry marked and side measures 14, 8, other sides unknown. parallelogram B with one longer side measuring 15 other sides unknown.

If we know the perimeter of each shape is 48 units and the dashed line through shape A is a line of symmetry, we can find the missing side lengths.

Shape B doesn’t have a line of symmetry, but if we were told that its opposite sides have equal lengths, then we can also reason about the three missing side lengths.

Problem 1 (Lesson 7)

  1. What is the perimeter of the rhombus? Explain or show your reasoning.

    rhombus. 4 sides of equal length. One side labeled 13 centimeters.
  2. Diego says he can find the area of this rectangle because he knows two side lengths.

    Do you agree with Diego? Explain your reasoning.

    rectangle. Top side, 19 feet. Bottom side, 19 feet.

Problem 2 (Lesson 8)

  1. Draw the lines of symmetry for the windmill blades.

    image of shape that looks like a windmill with 5 blades. Each blade, rectangle, length 5 feet, width 1 and 1 half feet. Center is pentagon.
  2. Each blade is 5 feet long and feet wide. What is the perimeter of the windmill? Explain or show your reasoning.

Problem 3 (Lesson 9)

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?

Problem 4 (Exploration)

How many lines of symmetry are there in this design? Explain or show how you know.

sun shaped design

Problem 5 (Exploration)

Make a shape or design with one or more lines of symmetry. Trade shapes with a partner and find all of the lines of symmetry of your partner’s shape. You may find pattern blocks helpful to make your shape or design.