Unit 8 Geometry Retake

Unit 8 Geometry Retake

By Joshua Parrish

Triangle Inequality Theorem

Sides of a triangle

• 3+4>5, 3+5>4, 5+4>3

• The sum of the shorter sides needs to be greater than the larger side.

• 3 + 4 < 9

Not a triangle

• 1 + 2 = 3

• Is not greater than 3

• Cannot form a triangle

Triangle

• 7, 13, 18

• Forms a triangle

• 7 + 13 = 20

• 20 > 18

Multiple Choice

Determine if the 3 numbers can be measures of the sides of a triangle. 9, 8, 10

• Yes

• No

Multiple Choice

Determine if the 3 numbers can be measures of the sides of a triangle. 9, 11, 20

• Yes

• No

Multiple Choice

Determine if the 3 numbers can be measures of the sides of a triangle. 9, 15, 26

• Yes

• No

Multiple Choice

Determine if the 3 numbers can be measures of the sides of a triangle. 4, 16, 19

• Yes

• No

Find missing angles in a Triangle

The Sum of the Angles of a Triangle

all 3 angles add to 180 degrees.

Multiple Choice

Find the measure of the missing angle.

• 139°
• 66°
• 138°
• 116°

Multiple Choice

Work out the size of the missing angle

• 22

• 202

• 20

• 158

Multiple Choice

A triangle's angles add up to...

• 90 Degrees
• 180 Degrees
• 360 Degrees
• OVER 9000 Degrees

Set up an equation to solve for x

Multiple Choice

Solve for x.

• 16

• 11

• 50

• 6

Circumference and Area of a Circle

Circle

The set of points equidistant from a given point called the center

Parts of a Circle

Circumference - the distance around the circle

Diameter - the distance across the circle, through the center

Radius - The distance from the center to any point on the circle

Multiple Choice

What does the red line represent?

• The circumference of the circle

• The diameter of the circle

• The radius of the circle

Radius and Diameter

The diameter is twice as long as the radius.

d = 2r

The radius is half the length of the diameter.

r = d/2

Multiple Choice

The diameter of a circle is 10 in.

What is its radius?

• 20 in.

• 5 in.

Pi

The ratio of a circle's circumference to its diameter.

Used to calculate the circumference and area of a circle.

Solve for C

Multiple Choice

Which ratio is used to calculate Pi?

• $$\frac{Circumference}{Radius}$$  

• $$\frac{Circumference}{Diameter}$$  

• $$\frac{Radius}{Circumference}$$  

• $$\frac{Diameter}{Circumference}$$  

Circumference

Solve a Circumference Problem

1. Write the formula

2. Substitute the values

3. Multiply

4. Write the unit of measure

Multiple Choice

Calculate the circumference of the circle. C =  $$\pi$$  d

• 98.91 ft.

• 63 ft.

• 197.82 ft.

Given a circle with a diameter of 63 ft.

calculate the circumference

Area of a Circle

Solve an Area of a Circle Problem

Multiple Choice

Does this circle show the radius or diameter?

• radius

• diameter

Multiple Choice

According to the Area of a Circle formula, do you need to know the radius or diameter? A =  $$\pi$$   $$r^2$$  

• radius

• diameter

Multiple Choice

What is the R of this circle?

• 40 cm

• 20 cm

• 10 cm

Multiple Choice

Calculate the Area of the circle.

A =  $$\pi$$   $$\cdot r\cdot r$$  

• 314 $$cm^2$$

• 62.8  $$cm^2$$  

• 1256  $$cm^2$$  

Given a circle with a diameter of 20 cm.

calculate the area.

Multiple Choice

What is the area of a circle with a radius of 8cm?

$$A=\pi\cdot r\cdot r$$  

• 200.96

• 25.12

• 50.24

Area - Trapezoid

Multiple Choice

What formula do we use to find the area of this shape?

• $$A\ =\frac{1}{2}bh$$

• $$A\ =\ \frac{\left(b_1\ +b_2\right)h}{2}$$

Multiple Select

What two sides are the bases? (Click on both of them)

• 7

• 4

• 6

• 8

• 5

Multiple Select

What is the height of this trapezoid?

• 7

• 4

• 6

• 8

• 5

Area of Triangles

How can you use the formula for the area of a parallelogram to find the area of a triangle?

Multiple Choice

What is the area of this triangle?

$$A=\frac{\left(bxh\right)}{2}$$  

• 49 square feet

• 600 square feet

• 100 square feet

• 300 square feet

Multiple Choice

What is the area of this triangle?

$$A=\frac{\left(bxh\right)}{2}$$  

• 216 square cm

• 200 square cm

• 108 square cm

• 180 square cm

Surface Area

Surface area= 2(lengthxwidth)+2(lengthxheight)+2(widthxheight)​

Multiple Choice

What is the surface area of this figure?

• 200 cm ²

• 800 cm ²

• 400 cm ²

• 100 cm ²

Multiple Choice

Find the Surface Area

• 556 cm²

• 278 cm²

• 680 cm²

• 340 cm²

Volume of a Prism

Vocabulary

• Prism - A Three dimensional object with two bases

• Pyramid - A Three dimensional object with one base that all come to the same point

• Volume - The amount of space a three dimensional object occupies

Formula for Volume of a Prism

V=LxWxH

L=Length

W=Width

H=Height

​

OR

​

V=Bh​

B= Area of the base

h= height of the prism

Multiple Choice

What is the volume of this rectangular prism?

$$V=LxWxH$$  

• 15 cm³

• 125 cm³

• 120 cm³

• 25 cm³

Multiple Choice

What is the volume of this prism?

$$V=LxWxH$$  

• 24 cubic cm

• 240 cubic cm

• 60 cubic cm

• 20 cubic cm

Multiple Choice

Find the volume:

$$V=\frac{\left(LxWxH\right)}{2}$$  

• 960 cm ³

• 240 cm ³

• 960 cm ²

• 1920 cm ³

Real World Application

Multiple Choice

1. Find Area of the bigger shape:

$$A=BxH$$  

2. Find Area of the smaller shape

$$A=BxH$$  

 

3. Subtract Area of big shape - Area of small shape

• 441 cm²
• 443 mm²

• 425 cm²
• 341 cm²

Multiple Choice

1. Find the Area of the rectangle

$$A=BxH$$  

2. Find the Area of the Circle (the diameter is 12)

$$A=\pi\cdot r\cdot r$$  

3. Subtract Area of rectangle-Area of circle

• 264 sq units

• 113.04 sq units

• 150.96 sq units

• 377.04 sq units

Cross Sections of

3-D Figures

By Reed Carbone

Definitions:

Cross Section: A cross section is like a slice of a 3-D figure. If you slice through a 3-D figure, the cross section is the shape of the slice.​

Subject | Subject

Some text here about the topic of discussion

​Visuals:

Multiple Choice

What is the cross section shown?

• Cone

• Triangle

• Sphere

• Circle

Multiple Choice

What is the 2D cross section of this image when cut vertically?

• Circle

• Trapezoid

• Triangle

• Square

Multiple Choice

What is the 2D cross section of this triangular pyramid?

• Trapezoid

• Triangle

• Rectangle

• Square