### 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.