Bell Work

• 1) Convert the following into the units given:

• a) 30 cm to mm b) 4.5 ft to in

• c) 18 yds to ft d) 555 cm to km

• e) 3 mi to ft f) 48 oz to lbs

Outcomes

• I will be able to:• 1) Find and simplify the ratio of two

numbers • 2) Understand what it means for objects to

be similar• 3) Use proportions to solve real life

problems, such as computing the width of a painting

Colosseum Activity

• Facts about the Colosseum: • Originally called the Flavian Amphitheatre, it was called

the Colosseum for the colossus (large statue) of Nero nearby.

• It was capable of seating 50,000 spectators. The large entrance arches allowed mass numbers of people to enter and exit in a short amount of time.

• Activities at the Colosseum included gladiator matches and animal hunts.

Colosseum Activity• 1) Measure the height of the colosseum and

one of the archways in the picture on your paper in inches(on your paper it says mm).

• Height of Colosseum in picture = _______ in

• Height of archway in picture = ________ in

• 2) Using the fact that the archways approximately measure, 23 feet, explain and find the approximate height of the actual Colosseum.

Colosseum Activity

• What is the approximate height of the Colosseum?

• How did you find it?

about 147 feet by my calculation

By setting up a proportion

x

23

1875.3

5. Cross multiply and solve.

Ratio and proportion 8.1

• For example, the ratio of 6:8 would be generally be written as: 3:4 because 2 goes into both 6 and 8.

a:b

a

b

units

we can express the ratio in simplified form.

Ratio and Proportion Examples

• 1. 2.

• ***We must convert to the same units• ***Always convert to the smallest units, so

we can multiply instead of divide.

39 cm

13 m

2 yards

12 feet

cm

m

m

cm

100

1

13

39 1300

39100

3

The answer will always just be a number without units!

***Try #2 on your own!

Examples

• 3. The perimeter of the rectangle ABCD shown below is 32 inches. The ratio of AB:BC is 3:5. What are the dimensions of the rectangle?

A B

D C

3x

5x5x

3x

***Remember, perimeter is all sidesadded together

3x + 5x + 3x + 5x = 32

x = 2

Extended Ratio• Extended Ratio (of angles): The

measures of the angles in are in a ratio according to their angle measurements. For instance, if we had a triangle that had measurements 30°, 60°, and 90°, it would be in an extended ratio of 30:60:90, or 1:2:3.

• Example:

x 2x

3x

Examples

• 1) The measure of the angles in ∆ABC are in the extended ratio of 1:1:2. Find the measures of the angles.

***Hint: Draw a picture and label the angles

x x

2x x + x + 2x = 1804x = 180

x = 45Are wefinished?

A B

C

90

45

45

C

B

A

Examples

• 2. The measure of the angles in quadrilateral EFGH are in the extended ratio of 2:2:1:1. What are the measures of the angles? What kind of quadrilateral is EFGH?

• ***Again, draw a picture

2x

x

2x

x

Similar Figures• Similar Figures – Figures that have the

exact same shape(equal angle measures), and their side lengths are proportional

Label what we know first!!!

3

5

4 How can wefind the missingpieces?

Similar Figures

Label what weknow first!

1215

How can we find the missingpieces?

If we go from big to small wemultiply. Fromsmall to big divide.

15

1215 ÷ 3 = 5

5

12 x 3 = 36

36

Does anyone know how to find the missing piece?

39

13

Proportionsequation

b and c

a and d

mean

mean extreme

extreme

Proportions

extremes

means So, ad = bc

reciprocals

So, c

d

a

b

Examples

• 1)

• 2)

• 3)

2

18x

yy

1

4

5

1

4

4

10

xx

Examples• 4. Phidias, an ancient architect and sculptor, created

Athena Parthenos around 438 BC. Athena Parthenos was made of gold and ivory, and it was housed inside the Parthenon in Athens, Greece. Unfortunately, the statue was lost around the 5th century, most likely to fire. On the left is a modern reconstruction of the statue, found in Nashville, Tennessee. It is said that Nike, the goddess of victory found in her right hand, is 6 feet tall. The ratio of Nike to Athena is 3:19. How tall is the statue of Athena Parthenos?

Examples• 5. The School of Athens, one of the most

famous paintings by Renaissance painter Raphael, depicts some of the greatest minds of the time: Plato, Aristotle, Socrates, and (our favorite) Pythagoras, among others. The real height is about 500 centimeters. Approximately how wide is the painting, in meters?

Exit?’s1. What are similar figures?

a) When two figures have the same # of sides

b) When two figures have the same angle measures

c) When two figures have proportional sides

d) When two figures have angles and sides that are about the same

e) Both b and c

Exit ?’s2. Which pair of figures are similar?

a) b)

• c) d)

Exit ?’s

3. How can you determine if two figures are similar?

a) Verify that all angle measures are the same

b) Check to make sure one side from each figure is the same

c) Check to see if all sides are proportional

d) See if the figures have the same number of sides

e) Both a and c

Exit ?’s4. What is a ratio?

a) The relationship in quantity or size of two or more things

b) The expression of relative values

c) The quotient of mathematical expressions

d) all of the above

e) none of the above

Exit ?’s5. What is a proportion?

a) statement of equality between two ratios

b) relation of parts to each other or the whole

c) an equal share

d) all of the above

e) none of the above