Unit 3 Review: Angles and Volume

​Unit 3 Review: Angles and Volume

​Concept #1 - Can it make a triangle?

​Angle Properties

The three interior angles of a triangle must add up to 180 degrees.

​Example 1​: 40, 60, 80 - Yes!

Example 2: ​20, 30, 120 - No!

​Side Properties

The sum of the two shortest sides must be GREATER than the length the longest side.

Example 1: 3, 4, 6 - Yes!

Example 2: 5, 5, 12 - No​!

Multiple Choice

Would the following characteristics form a triangle?

Angle 1 = 60 degrees, Angle 2 = 70 degrees, Angle 3 = 50 degrees

• Yes, the 3 angles have a sum of 180 degrees.

• No, the 3 angles do not have a sum of 180 degrees.

Multiple Choice

Would the following characteristics form a triangle?

Angle 1 = 20 degrees, Angle 2 = 80 degrees, Angle 3 = 100 degrees

• Yes, the 3 angles have a sum of 180 degrees.

• No, the 3 angles do not have a sum of 180 degrees.

Multiple Choice

Would the following characteristics form a triangle?

Angle 1 = 100 degrees, Angle 2 = 15 degrees, Angle 3 = 65 degrees

• Yes, the 3 angles have a sum of 180 degrees.

• No, the 3 angles do not have a sum of 180 degrees.

Multiple Choice

Would the following characteristics form a triangle?

Side 1 = 4 units, Side 2 = 6 units, Side 3 = 9 units

• Yes, the sum of the two shorter sides is greater than the longest side.

• No, the sum of the two shorter sides is NOT greater than the longest side.

Multiple Choice

Would the following characteristics form a triangle?

Side 1 = 12 units, Side 2 = 3 units, Side 3 = 5 units

• Yes, the sum of the two shorter sides is greater than the longest side.

• No, the sum of the two shorter sides is NOT greater than the longest side.

Multiple Choice

Would the following characteristics form a triangle?

Side 1 = 5 units, Side 2 = 1 units, Side 3 = 11 units

• Yes, the sum of the two shorter sides is greater than the longest side.

• No, the sum of the two shorter sides is NOT greater than the longest side.

Multiple Choice

A triangle has been created.

Angle 1 = 45 degrees, Angle 2 = 82 degrees, Angle 3 = x degrees.

Which equation could model the relationship between the 3 angles?

• 45 + 82 + x = 180

• 45 + 82 = x

• 45 + 82 + x = 90

Multiple Choice

A triangle has been created.

Angle 1 = 45 degrees, Angle 2 = 82 degrees, Angle 3 = x degrees.

What is the value of x?

• 53

• 98

• 127

• 37

Multiple Choice

A triangle has been created.

Angle 1 = 74 degrees, Angle 2 = x degrees, Angle 3 = x + 8 degrees.

Which equation could model the relationship between the 3 angles?

• 2x + 82 = 180

• 74 + x = x + 8

• 2x + 82 = 90

• x + 74 = 180

Multiple Choice

A triangle has been created.

Angle 1 = 74 degrees, Angle 2 = x degrees, Angle 3 = x + 8 degrees.

What is the value of x?

• x = 49

• x = 106

• x = 104

• x = 37

Multiple Choice

A triangle has been created.

Angle 1 = 74 degrees, Angle 2 = x degrees, Angle 3 = x + 8 degrees.

How many degrees is angle 3?

• 57 degrees

• 53 degrees

• 74 degrees

• 180 degrees

Angles that have a sum of 180 degrees.​

​Supplementary Angles

Angles that have a sum of 90 degrees.​

​Complementary Angles

​Concept #2: Angle Properties

S

In the image above, Angle PRS and and Angle QRT are vertical angles​

Created when lines intersect. Vertical angles share a vertex and are "opposite" one another. Vertical angles are always equal.​

​Vertical Angles

​Concept #2: Angle Properties

S

Multiple Choice

What equation could model the relationship between Angle TQS and Angle RQS?

• 38 + (9x - 2) = 180

• 38 + (9x - 2) = 90

• 38 = 9x - 2

Multiple Choice

What is the value of x?

• x = 6

• x = 4

• x = 5

• x = 52

Multiple Choice

How many degrees is angle TQS?

• 52 degrees

• 6 degrees

• 90 degrees

• 38 degrees

Multiple Choice

What equation would model the relationship between Angle AGC and Angle BGD?

• 140 = 3x - 1

• 140 + (3x - 1) = 180

• 140 + (3x - 1) = 90

Multiple Choice

What is the value of x?

• x = 47

• x = 140

• x = 46

• x = 48

Multiple Choice

What equation would model the relationship between Angle DGE and Angle EGF?

• 8x + 60 = 180

• 8x + 60 = 90

• 8x = 60

Multiple Choice

What is the value of x?

• x = 15

• x = 120

• x = 30

• x = 7.5

Multiple Choice

What is the measure of Angle DGE?

• 120 degrees

• 15 degrees

• 60 degrees

• 7.5 degrees

Find the area of the base, then multiply by the height, then divide by 3.

​Pyramids

Find the area of the base, then multiply by the height​

​Prisms

​Concept #3: Volume of Prisms and Pyramids

Multiple Choice

What is the volume of the figure shown?

• 20 cubic yds

• 60 cubic yds

• 12 cubic yds

• 32 cubic yds

Multiple Choice

What is the volume of the figure shown?

• 12 cubic inches

• 36 cubic inches

• 9 cubic inches

• 21 cubic inches

Multiple Choice

What is the volume of the figure shown?

• 2 cubic feet

• 6 cubic feet

• 12 cubic feet

• 4 cubic feet

Multiple Choice

What is the volume of the figure shown?

• 8 cubic cm

• 6 cubic cm

• 2.6 cubic cm

• 4 cubic cm

Multiple Choice

What is the volume of the figure shown?

• 252 cubic yd

• 84 cubic yd

• 19 cubic yd

• 294 cubic yd

Multiple Choice

What is the volume of the figure shown?

• 64 cubic mm

• 128 cubic mm

• 21.3 cubic mm

• 42.7 cubic mm

Multiple Choice

What is the volume of the figure shown?

• 30 cubic in

• 60 cubic in

• 20 cubic in

• 10 cubic in

​Concept #4: Surface Area

​Surface Area

The sum of the area of all faces of figure.​

Some text here about the topic of discussion

Multiple Choice

What is the surface area of the figure shown?

• 72 square ft

• 32 square ft

• 48 square ft

• 10.7 square ft

Multiple Choice

What is the surface area of the figure shown?

• 2416 square yd

• 3840 square yd

• 805.3 square ft

• 2432 square yd

Multiple Choice

What is the surface area of the figure shown?

• 416 square in

• 512 square in

• 396 square in

• 492 square yd

Multiple Choice

What is the surface area of the figure shown?

• 4466 square ft

• 5306 square ft

• 4947 square ft

• 5787 square ft