# 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.

### Problem 1

#### Pre-unit

Practicing Standards:  3.G.A.1

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

### Solution

For access, consult one of our IM Certified Partners.

### 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

For access, consult one of our IM Certified Partners.

### 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

For access, consult one of our IM Certified Partners.

### Problem 4

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

### Solution

For access, consult one of our IM Certified Partners.

### Problem 5

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

For access, consult one of our IM Certified Partners.

### Problem 6

Here are 3 rhombuses:

1. What attributes do the rhombuses share?
2. What attributes are different in the three rhombuses?

### Solution

For access, consult one of our IM Certified Partners.

### Problem 7

Draw the lines of symmetry for these letters:

### Solution

For access, consult one of our IM Certified Partners.

### Problem 8

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

### Solution

For access, consult one of our IM Certified Partners.

### Problem 9

#### Exploration

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

### Solution

For access, consult one of our IM Certified Partners.

### Problem 10

#### Exploration

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

• rectangle
• rhombus
• square

### Solution

For access, consult one of our IM Certified Partners.

### Problem 1

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

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.

### Solution

For access, consult one of our IM Certified Partners.

### 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.

### Solution

For access, consult one of our IM Certified Partners.

### 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

For access, consult one of our IM Certified Partners.

### Problem 4

#### Exploration

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

### Solution

For access, consult one of our IM Certified Partners.

### 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

For access, consult one of our IM Certified Partners.