# Lesson 8 Cavalieri to the Rescue Solidify Understanding

Define each figure by answering each question.

### 1.

parallelogram

#### a.

How many sides?

#### b.

Which sides are

#### c.

Which sides are

#### d.

How many lines of symmetry?

#### e.

What is the measure of the smallest angle of rotational symmetry?

### 2.

octagon (regular)

#### a.

How many sides?

#### b.

Which sides are

#### c.

Which sides are

#### d.

How many lines of symmetry?

#### e.

What is the measure of the smallest angle of rotational symmetry?

### 3.

trapezoid

#### a.

How many sides?

#### b.

Which sides are

#### c.

Which sides are

#### d.

How many lines of symmetry?

#### e.

What is the measure of the smallest angle of rotational symmetry?

### 4.

rhombus

#### a.

How many sides?

#### b.

Which sides are

#### c.

Which sides are

#### d.

How many lines of symmetry?

#### e.

What is the measure of the smallest angle of rotational symmetry?

### 5.

pentagon (regular)

#### a.

How many sides?

#### b.

Which sides are

#### c.

Which sides are

#### d.

How many lines of symmetry?

#### e.

What is the measure of the smallest angle of rotational symmetry?

### 6.

rectangle

#### a.

How many sides?

#### b.

Which sides are

#### c.

Which sides are

#### d.

How many lines of symmetry?

#### e.

What is the measure of the smallest angle of rotational symmetry?

### 7.

square

#### a.

How many sides?

#### b.

Which sides are

#### c.

Which sides are

#### d.

How many lines of symmetry?

#### e.

What is the measure of the smallest angle of rotational symmetry?

### 8.

hexagon (regular)

#### a.

How many sides?

#### b.

Which sides are

#### c.

Which sides are

#### d.

How many lines of symmetry?

#### e.

What is the measure of the smallest angle of rotational symmetry?

### 9.

Calculate the perimeter and the area of each quadrilateral.

#### a.

perimeter:

area:

#### b.

perimeter:

area:

#### c.

perimeter:

area:

### 10.

Compare and contrast your answers in problem 9. What do you notice about the areas and perimeters? Write a statement about your observations.

### 11.

The figure contains several triangles. Consider

Given that

### 12.

The figure shows a cube with edges of length

#### a.

Write an expression for the volume of the entire cube in terms of

#### b.

Into how many pieces is the cube cut?

#### c.

How many of these pieces are also cubes? Write an expression in terms of

#### d.

How many pieces have a volume of

#### e.

How many pieces have a volume of

#### f.

Write the volume of the figure as the sum of the volumes of its pieces. (Count them in the diagram.)

#### g.

Show that your answers in

### 13.

If the cubes and rectangular prisms in problem 12 were rearranged, would the new figure have the same volume? Explain your reasoning.

### 14.

Use Cavalieri’s principle to explain why a perfect stack of playing cards has the same volume as one that has been bumped sideways.

Determine if each pair of solids is similar, congruent, or neither. Justify your answers.

### 15.

Similar

Congruent

Neither

### 16.

Similar

Congruent

Neither

### 17.

Similar

Congruent

Neither

### 18.

Similar

Congruent

Neither

### 19.

Similar

Congruent

Neither

### 20.

Similar

Congruent

Neither

### 21.

Similar

Congruent

Neither