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