Chapter 7,9,8 Study Guide

Chapter 7,9 Study Guide

Angles

Congruent Angles: angles that are equal (have the same measure)

Adjacent Angles : angles that are next to each other

Vertical Angles: angles across from each other

Complementary Angles: angles that have a SUM of 90 degrees

Supplementary Angles: angles that have a SUM of 180 degrees

COMPLEMENTARY ALWAYS ADD UP TO 90 degrees

SUPPLEMENTARY ALWAYS ADD UP TO 180 degrees

Multiple Choice

Which names a pair of adjacent angles?

• ∠CXD and ∠FXE
• ∠CXF and ∠DXE
• ∠CXD and ∠DXE

Multiple Choice

Which are pairs of adjacent angles?

• ∠COB & ∠DOA
• ∠AOD & ∠AOC
• ∠COB & ∠AOD
• ∠BOD & ∠AOC

Multiple Choice

What is the measure of the missing angle?

• 76
• 66
• 156
• 154

Multiple Choice

If m∠1 = 30°, then m∠3 = 

• 30°
• 60°
• 150°
• undetermined

Multiple Choice

Congruent is another word for

• small
• equal
• vertical
• long

Multiple Choice

∠1 and ∠3 can best be described as -

• complementary angles
• supplementary angles
• vertical angles
• adjacent angles

Multiple Choice

Angles 4 and 2 are what angle pair?

• Complementary
• Supplementary
• Adjacent
• Vertical

Multiple Choice

What are complementary angles?

• Angles that add up to 180°
• Angles that add up to 90°
• Angles that are equal to each other
• Angles that are opposite of each other when lines intersect.

Multiple Choice

What are supplementary angles?

• Angles that add up to 180°
• Angles that add up to 90°
• Angles that are equal to each other
• Angles that are opposite of each other when lines intersect

Multiple Choice

If angle ∠ABD is 67°. What is ∠DBC?

• 180°
• 90°
• 67°
• 23°

Multiple Choice

Find the missing angle.

• 47
• 37
• 57
• 137

ANGLES

parallel lines: two lines that NEVER intersect and have the same slope

perpendicular lines: two lines that intersect at 90 degrees

transversal: a line cutting or intersecting a system of lines

vertical angles: formed by two intersecting lines, opposite each other

corresponding angles: lie on the same side of the transversal in the same spot

alternate interior: lie inside pair of lines but OPPOSITE side of transversal

alternate exterior: lie outside pair of lines but OPPOSITE side of transversal

Multiple Choice

What relationship exists between angles 1 and 5

• Corresponding angles

• Supplementary angles

• Vertical angles

• Alternate Exterior Angles

Multiple Choice

What relationship exists between angles 2 and 3

• Corresponding angles

• Supplementary angles

• Vertical angles

• Alternate Exterior Angles

Multiple Choice

Angles 4 and 6 are...

• supplementary

• congruent

Multiple Choice

 $\angle1$  and  $\angle2$  are ___.  

• Alternate Interior Angles

• Alternate Exterior Angles

• Same-side Interior Angles

• Corresponding Angles

• None of these

Multiple Choice

Name the angle relationship.

• Alternate Interior
• Alternate Exterior
• Corresponding
• Vertical Angles

Multiple Choice

Name the angle relationship.

• Alternate Interior
• Alternate Exterior
• Corresponding
• Vertical Angles

Multiple Choice

Which of the following is an example of corresponding angles?

•  $\angle8\ and\ \angle4$  

•  $\angle5\ and\ \angle7$  

•  $\angle1\ and\ \angle7$  

•  $\angle3\ and\ \angle5$  

Multiple Choice

Which of the following angles would NOT be congruent to the measure of  $\angle7$ ?

•  $\angle2$  

•  $\angle3$  

•  $\angle6$  

•  $\angle8$  

Multiple Choice

Angle 6 and Angle 7 are examples of which type of angle pair?

• Alternate exterior angles

• Alternate interior angles

• Vertical angles

• Corresponding angles

Multiple Choice

Angle 1 and Angle 5 are examples of which type of angle pair?

• Alternate exterior angles

• Alternate interior angles

• Vertical angles

• Corresponding angles

Multiple Choice

Angle 3 and Angle 6 are examples of which type of angle pair?

• Alternate exterior angles

• Alternate interior angles

• Vertical angles

• Corresponding angles

TRIANGLE THEOREM

TRIANGLE INTERIOR ANGLE SUM THEOREM : all angles add to a total of 180 degrees

the sum of the measures of the angles of a triangle always add up to 180 degrees

TRIANGLE EXTERIOR ANGLE SUM THEOREM: exterior angle is congruent to the sum of the measures of the nonadjacent interior angles

Multiple Choice

What is the value of the missing angle?

• 90

• 100

• 20

• 120

Multiple Choice

What is the value of the missing angle?

• 105

• 80

• 55

• 25

Multiple Choice

Which of the following terms best describes Angle d?

• Remote interior angle
• Corresponding angle
• Exterior angle
• Interior angle

Multiple Choice

Find the measure of the missing angle.

• 90^o
• 10⁰
• 130^o
• 50^o

Multiple Choice

What is the third angle of a triangle whose 1st angle is 79 and the 2nd angle is 43?

• 43
• 58
• 72
• 101

Multiple Choice

The Triangle Sum Theorem states that the sum of all angles in a triangle is ______. 

• 45°
• 90°
• 180°
• 360°

Multiple Choice

Find the measure of the angle indicated. 

• 139°
• 66°
• 138°
• 116°

polygons: closed (non gaps or openings) figure composed of straight lines

POLYGON ANGLE SUM: 180(n-2) n- number of sides

Triangle : 3 sides

quadrilateral: 4 sides

pentagon: 5 sides

hexagon: 6 sides

heptagon: 7 sides

octagon: 8 sides

nonagon: 9 sides

decagon: 10 sides

dodecagon: 12 sides

Multiple Choice

What is the sum of the interior angles of the hexagon shown?

• 180° 
• 540° 
• 720° 
• 1080° 

Multiple Choice

What is the SUM of the angle measures in a triangle (3 sides)?

• 60°
• 90°
• 120°
• 180°

Multiple Choice

What is the SUM of the angle measures in a nonagon (9 sides)?

• 1440°
• 900°
• 1080°
• 1260°

Multiple Choice

Solve for x. 

• 100
• 120
• 125
• 130

Multiple Choice

Find the sum of the interior angles of a nonagon.

• 1260
• 900
• 1620
• 180

3D Figures

Solid: do not lie flat in a plane - 3 dimensional, have length width and height

prism: solid with two congruent, parallel bases and parallelogram faces

pyramid: solid with one base which is a polygon

cylinder: solid with two bases that are parallel, congruent circles

cone: solid with one circular base and 1 vertex

polyhedron: solids whose faces are polygons

parallel lines: lines that never cross

skew lines: do not intersect but are not parallel lines

Face, Bases, Edge, Vertex

• face: flat surface of solid

• base: surface solid stands on

• edge: where two faces meet

• vertex: where two edges meet

Multiple Choice

What is shown in the picture?

• faces

• bases

• edges

• vertices

Multiple Choice

What is shown in the picture?

• face

• base

• edge

• vertex

Multiple Choice

What is shown in the picture?

• face

• base

• edge

• vertex

Multiple Choice

What is shown in the picture?

• face

• base

• edge

• vertex

Multiple Choice

Number of Vertices?

• 3
• 4
• 5
• 6

Multiple Choice

Number of Faces?

• 7
• 5
• 4
• 15

Multiple Choice

How many edges in this shape?

• 2
• 4
• 6
• 8

Multiple Choice

How many vertices in this shape?

• 3
• 4
• 5
• 6

Multiple Choice

How many flat faces in this shape?

• 3
• 4
• 5
• 6

Multiple Choice

How many straight edges in this shape?

• 0
• 1
• 2
• 3

Multiple Choice

How many vertices in this shape?

• 0
• 1
• 2
• 3

Multiple Choice

How many edges in this shape?

• 8
• 6
• 4
• 12

Multiple Choice

How many flat faces in this shape?

• 1
• 2
• 3
• 4

Multiple Choice

How many vertices in this shape?

• 8
• 6
• 4
• 12

Multiple Choice

How many faces in this shape?

• 8
• 6
• 4
• 12

Volume

• volume of a 3d figure is the measure of space on the inside

• measured in cubic units

AREA AND CIRCUMFERENCE OF CIRCLE

VOLUME OF CYLINDER

SQUARE PYRAMIDS

VOLUME OF CONE

VOLUME AND SURFACE AREA OF SPHERE

Multiple Choice

How do you find the volume of a cylinder?

• V= ^1/₃ πr²h
• V= ^4/₃ πr²h
• V= ^4/₃ πr³
• V= πr²h

Multiple Choice

How do you find the volume of a cone?

• V= ^1/₃ πr²h
• V= ^4/₃ πr²h
• V= ^4/₃ πr³
• V= πr²h

Multiple Choice

How do you find the volume of a sphere?

• V= ^1/₃ πr²h
• V= ^4/₃ πr²h
• V= ^4/₃ πr³
• V= πr²h

Multiple Choice

What is volume?

• The amount of space of a 2-D object
• The amount of space in a 3-D object
• Water
• Area

Multiple Choice

Find the volume of the cylinder. Round your answers to the nearest tenth if necessary. Use 3.14 for π. The radius is 2 cm and the height is 2.5 cm.

• 16.4 cm³
• 31.7 cm³
• 31.4 cm³
• 22.0 cm³

Multiple Choice

 Find the volume if the diameter is 12 m and the height is 10 m.

• 72
• 66
• 1130.4
• 90

Multiple Choice

Find the volume

• 960 cm ³
• 240 cm ³
• 960 cm ²
• 1920 cm ³

Multiple Choice

Find the volume

• 96cm³
• 54cm³
• 80cm³
• 24cm³

Multiple Choice

Find the volume of the figure. Round to the nearest tenth. 

• 80 cm³
• 40 cm²
• 80 cm²
• 40 cm³

Multiple Choice

Find the volume if the dimensions are 8 in x 15 in x 18 in

• 210 in³
• 260 in³
• 2160 in³
• 2610 in³

Multiple Choice

For a sphere with a radius of 8, what is the Surface Area?

• 803.84

• 10096.2304

• 2143.573

• 100.48

Multiple Choice

Find the surface area.

• 6658.56 mm²

• 452.16 mm²

• 904.32 mm²

• 108.8 mm²

Multiple Choice

A sphere has the radius of 5 meters. Find the volume. Use 3.14 for pi.

• 523.3 m³
• 104.7 m³
• 130.8 m³
• 1570 m³

Multiple Choice

Jack wants to know how much water a sphere can hold with a radius of 8 cm. Find the volume. Use 3.14 for pi.

• 83.6 cm³
• 2144.7 cm³
• 254 cm³
• 2220 cm³

Multiple Choice

Barney wanted to know how much ice cream he got in one scoop. The radius of a scoop is 2 inches. Find the volume. Use 3.14 for pi.

• 345.3 in³
• 33.5 in³
• 25.1 in³
• 50.2 in³

Multiple Choice

What is the volume of a sphere with the radius of 4 inches ? Use 3.14 for pi.

• 561.5 in³
• 267.9 in³
• 201 in³
• 803.8 in³