4.8 Properties of Two-dimensional Shapes

Unit Goals

  • Students classify triangles and quadrilaterals based on the properties of their side lengths and angles, and learn about lines of symmetry in two-dimensional figures. They use their understanding of these attributes to solve problems, including problems involving perimeter and area.

Section A Goals

  • Classify triangles (including right triangles), parallelograms, rectangles, rhombuses, and squares based on the properties of their side lengths and angles.
  • Identify and draw lines of symmetry in two-dimensional figures.

Section B Goals

  • Solve problems involving unknown side lengths, perimeter, area, and angle measurements using the known attributes and properties of two-dimensional shapes.
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Section A: Side Lengths, Angles, and Lines of Symmetry

Problem 1

Pre-unit

Practicing Standards:  3.G.A.1

6 shapes.

  1. Which shapes are quadrilaterals?
  2. Which shapes are rhombuses?
  3. Which shapes are rectangles?

Solution

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Problem 2

Pre-unit

Practicing Standards:  3.MD.C.7, 3.MD.D.8

Find the perimeter and area of the rectangle. Explain or show your reasoning.

rectangle, length, 13. Width, 6.

Solution

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Problem 3

Pre-unit

Practicing Standards:  3.G.A.2

Select all images that show half of the shaded rectangle.

A:  

B:  

C:  

D:  

E:  

Solution

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Problem 4

4 shapes. All have 4 sides.

  1. Name some attributes that these shapes share.
  2. Name some attributes that the shapes do not share.

Solution

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Problem 5

4 triangles, all have 3 sides of different length. A. 1 obtuse angle, 2 acute angles. B. 3 acute angles. C and D. 1 right angle, 2 acute angles.

  1. Which of the triangles are right triangles?
  2. Which of the triangles have an obtuse angle?
  3. Which of the triangles have 3 acute angles?

Solution

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Problem 6

Here are 3 rhombuses:

3 rhombuses. all have opposite sides parallel and same length, opposite angles equal size. A, B, 2 acute, 2 obtuse angles. C, 4 right angles.
  1. What attributes do the rhombuses share?
  2. What attributes are different in the three rhombuses?

Solution

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Problem 7

Draw the lines of symmetry for these letters:

6 figures with the shapes of the capital letters, A, C, G, N, O, Z.

Solution

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Problem 8

Complete each figure so that the dashed line is a line of symmetry for the new figure.

triangle on grid. The horizontal side overlaps a dashed line of symmetry.
parallelogram, right side overlapping a dashed line.

Solution

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Problem 9

Exploration

Draw all the lines of symmetry you can find in this snowflake. How many can you find?

drawing of a snowflake with 6 equal parts. symmetric down the middle with 3 petals on each side.

Solution

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Problem 10

Exploration

Draw each shape and all the lines of symmetry you can find in it.

  • rectangle
  • rhombus
  • square

Solution

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Section B: Reason about Attributes to Solve Problems

Problem 1

  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.

Solution

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Problem 2

  1. Draw the lines of symmetry for the windmill blades.
  2. Each blade is 5 feet long and \(1 \frac{1}{2}\) feet wide. What is the perimeter of the windmill? Explain or show your reasoning.
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.

Solution

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Problem 3

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?

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

Solution

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Problem 4

Exploration

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

Solution

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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.

Solution

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