10.10.6: Chapter Review

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Chapter Review

Points, Lines, and Planes

Use the figure shown for the following exercises.
$A line with four points, A, B, C, and D marked on it.$

Find /**/\overrightarrow {BC} \cup \overrightarrow {CD}/**/.

Find /**/\overline {AC} \cap \overline {BC}/**/.

Name the points in the set /**/\overrightarrow {BD} \cap \overleftarrow {CA}/**/.

Angles

Given that /**/{l_1}/**/ and /**/{l_2}/**/ are parallel lines, solve the angle measurements for all the angles in the figure shown.
$Two parallel horizontal lines are intersected by a transversal. The transversal makes four angles labeled 1, 2, 3, and 120 degrees with the line at the top. The transversal makes four angles numbered 5, 6, 7, and 8 with the line at the bottom. 1, 2, 7, and 8 are exterior angles. 3, 120 degrees, 5, and 6 are interior angles.$

Find the measure of the vertical angles in the figure shown.
$Two lines intersect each other forming four angles. One set of opposite angles is labeled (5 x plus 8) degrees and (6 x minus 7) degrees.$

Classify the angle as acute, right, or obtuse: /**/{79^ \circ }/**/.

Use the given figure to solve for the angles.
$A horizontal line and a vertical line intersect each other forming a right angle. A line originates from the intersection of the horizontal and vertical lines. This line makes an angle, 3 x plus 1 degrees with the horizontal line. This line makes an angle, 7 x plus 12 degrees with the vertical line.$

Use the given figure to solve for the angle measurements.
$A horizontal line with two lines originating from its center. The first ray makes an angle, 6 x minus 14 degrees with the horizontal line. The angle formed between the two rays is labeled 9 x plus 4 degrees. The second ray makes an angle, 6 x plus 1 degrees with the horizontal line.$

Triangles

Use the given figure to find the measure of the unknown angles.
$A right triangle with its interior angles marked x, 90 degrees, and 34 degrees.$

10.

Use algebra to find the measure of the angles in the figure shown.
$A triangle with its interior angles marked (x plus 10) degrees, (x minus 10) degrees, and x.$

11.

The two triangles shown are congruent by what theorem?
$Two triangles. The left side of the first triangle and the bottom side of the second triangle are congruent. The left side of the second triangle and the right side of the first triangle are congruent. The top angle of the first triangle and the bottom-left angle of the second triangle are congruent.$

12.

The two triangles shown are congruent by what theorem?
$Two triangles. The left side of the first triangle and the top side of the second triangle are congruent. The right side of the first triangle and the bottom side of the second triangle are congruent. The bottom side of the first triangle and the left side of the second triangle are congruent.$

13.

The two triangles shown are congruent by what theorem?
$Two triangles. The left side of the first triangle and the top side of the second triangle are congruent. The top-right angle of the first triangle and the top-left of the second triangle are congruent. The bottom-right angle of the first triangle and the bottom-left angle of the second triangle are congruent.$

14.

Are the two figures shown similar?
$Two smiley faces. The first one is smaller and the second one is bigger.$

15.

Are the two triangles shown similar?
$Two triangles. The sides of the first triangle are marked 16, 8, and 12. The sides of the second triangle are marked 6, 8, and 4.$

16.

Find the scaling factor of the two similar triangles in the given figure.
$Two triangles. The sides of the first triangle are marked 16, 8, and 64 over 3. The sides of the second triangle are marked 3, 8, and x.$

17.

Find the length of /**/x/**/ in the figure shown.

Polygons, Perimeter, and Circumference

Identify the polygons.

18.

$A polygon with six equal sides.$

19.

$A polygon with four equal sides and no right angles. Two diagonal lines run through the polygon.$

20.

$A polygon with eight equal sides.$

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.
$A triangle with its sides marked 3 x, 3 x plus 1, and 2 x plus 1.$

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.
$A quadrilateral with its angles marked (13 x plus 3) degrees, (11 x plus 1) degrees, 72 degrees, and (7 x plus 5) degrees.$

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?
$A tessellation pattern is made up of 8 hexagons.$

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.
$A parallelogram with its length marked 20 centimeters and height marked 13 centimeters.$

40.

If the area of a trapezoid equals /**/\frac45{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?
$A figure shows a semicircle placed on top of a rectangle. The length and width of the rectangle are 6 feet and 4 feet.$

44.

Find the area of the shaded region in the given figure.

$A circle is enclosed within a rectangle. The length of the rectangle is marked L equals 42 centimeters. The diameter of the circle is marked 20 centimeters. The circle touches the top and bottom sides of the rectangle.$

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.
$A right triangle. The legs are marked 6 and 12. The hypotenuse is marked c. The angle formed by the horizontal leg and hypotenuse is marked 60 degrees.$

52.

Find the measure of the unknown side and angle.
$A right triangle. The legs are marked 3.44 and 7. The hypotenuse is marked c. The angle formed by the horizontal leg and hypotenuse is marked theta.$

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Chapter Review

Points, Lines, and Planes