### 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.