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.
Section A: Side Lengths, Angles, and Lines of Symmetry
Problem 1
Pre-unit
Practicing Standards: 3.G.A.1
- Which shapes are quadrilaterals?
- Which shapes are rhombuses?
- Which shapes are rectangles?
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
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.
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
Problem 3
Pre-unit
Practicing Standards: 3.G.A.2
Select all images that show half of the shaded rectangle.
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
Problem 4
- Name some attributes that these shapes share.
- Name some attributes that the shapes do not share.
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
Problem 5
- Which of the triangles are right triangles?
- Which of the triangles have an obtuse angle?
- Which of the triangles have 3 acute angles?
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
Problem 6
Here are 3 rhombuses:
- What attributes do the rhombuses share?
- What attributes are different in the three rhombuses?
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
Problem 7
Draw the lines of symmetry for these letters:
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
Problem 8
Complete each figure so that the dashed line is a line of symmetry for the new figure.
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
Problem 9
Exploration
Draw all the lines of symmetry you can find in this snowflake. How many can you find?
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
Problem 10
Exploration
Draw each shape and all the lines of symmetry you can find in it.
- rectangle
- rhombus
- square
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
Section B: Reason about Attributes to Solve Problems
Problem 1
-
What is the perimeter of the rhombus? Explain or show your reasoning.
-
Diego says he can find the area of this rectangle because he knows two side lengths.
Do you agree with Diego? Explain your reasoning.
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
Problem 2
- Draw the lines of symmetry for the windmill blades.
- 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.
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
Problem 3
Here is a rectangle R.
-
What shape can be folded along a line of symmetry to give R? What are the side lengths of that shape?
- What shape can be folded twice along lines of symmetry to give R? What are its side lengths?
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
Problem 4
Exploration
How many lines of symmetry are there in this design? Explain or show how you know.
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
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
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.