Contemporary Mathematics

# Chapter Review

## Points, Lines, and Planes

Use the figure shown for the following exercises.
1 .
Find $\overrightarrow {BC} \cup \overrightarrow {CD}$.
2 .
Find $\overline {AC} \cap \overline {BC}$.
3 .
Name the points in the set $\overrightarrow {BD} \cap \overleftarrow {CA}$.

## Angles

4 .
Given that ${l_1}$ and ${l_2}$ are parallel lines, solve the angle measurements for all the angles in the figure shown.
5 .
Find the measure of the vertical angles in the figure shown.
6 .
Classify the angle as acute, right, or obtuse: ${79^ \circ }$.
7 .
Use the given figure to solve for the angles.
8 .
Use the given figure to solve for the angle measurements.

## Triangles

9 .
Use the given figure to find the measure of the unknown angles.
10 .
Use algebra to find the measure of the angles in the figure shown.
11 .
The two triangles shown are congruent by what theorem?
12 .
The two triangles shown are congruent by what theorem?
13 .
The two triangles shown are congruent by what theorem?
14 .
Are the two figures shown similar?
15 .
Are the two triangles shown similar?
16 .
Find the scaling factor of the two similar triangles in the given figure.
17 .
Find the length of $x$ in the figure shown.

## Polygons, Perimeter, and Circumference

Identify the polygons.
18 .
19 .
20 .
21 .
Find the perimeter of a regular hexagon with side length 5 cm.
22 .
The perimeter of a triangle is 18 in the given figure. Find the length of the sides.
23 .
What is the measure of an interior angle of a regular heptagon?
24 .
What is the measure of an interior angle of a regular octagon?
25 .
Calculate the measure of each interior angle in the figure shown.
26 .
Find the measure of an exterior angle of a regular pentagon.
27 .
What is the sum of the measures of the exterior angles of a regular heptagon?
28 .
Find the circumference of a circle with radius 3.2 cm.
29 .
Find the diameter of a circle with a circumference of 35.6 in.

## Tessellations

30 .
In what field of mathematics does the topic of tessellations belong?
31 .
Tessellations can have no _______or _________.
32 .
What type of transformation moves an object over horizontally by some number of units?
33 .
What type of transformation results in a mirror image of the shape?
34 .
Which regular polygons will tessellate the plane by themselves?
35 .
The sum of the interior angles of the shapes meeting at a vertex is equal to how many degrees?
36 .
How would you name this tessellation?

## Area

37 .
What is the area of a triangle with a base equal to 5 cm and a height equal to 12 cm?
38 .
If the area of a triangle equals $24{\text{ cm}}^2$ and the base equals 8, what is the height?
39 .
Find the area of the parallelogram shown.
40 .
If the area of a trapezoid equals $\frac{{45}}{2}{\text{ cm}}^2$, ${b_1} = 3{\text{ cm}}$, and the height equals $h = 5{\text{ cm}}$, find the length of ${b_2}$.
41 .
Find the area of an octagon if the apothem equals 10 cm and the side length is 12 cm.
42 .
The area of a circle is $50.3{\text{ in}}^2$. What is the radius?
43 .
You want to install a tinted protective shield on this window. How many square feet do you order?
44 .
Find the area of the shaded region in the given figure.

## Volume and Surface Area

45 .
Find the surface area of a hexagonal prism with side length 5 cm, apothem 3.1 cm, and height 15 cm.
A triangular prism has an equilateral base and side lengths of 15 in, triangle height of 10 in, and prism length of 25 in.
46 .
Find the surface area of the triangular prism.
47 .
Find the volume of the triangular prism.
48 .
Find the volume of a right cylinder with radius equal to 1.5 cm and height equal to 5 cm.
A right cylinder has a radius of 6 cm and a height of 10 cm.
49 .
Find the surface area of the right cylinder.
50 .
Find the volume of the right cylinder.

## Right Triangle Trigonometry

51 .
Find the lengths of the missing sides in the figure shown.
52 .
Find the measure of the unknown side and angle.
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