Transcript 8.1x - My Haiku

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?
about 147 feet by my calculation
• How did you find it?
By setting up a proportion
.5
23

3.1875 x
Cross multiply and solve.
Ratio and proportion 8.1
a
b
a:b
units
we can express the ratio in simplified form.
• For example, the ratio of 6:8 would be
generally be written as: 3:4 because 2
goes into both 6 and 8.
Ratio and Proportion Examples
• 1. 39 cm
13 m
2.
2 yards
12 feet
• ***We must convert to the same units
• ***Always convert to the smallest units, so
we can multiply instead of divide.
3
39
39cm
1m



13m 100cm 1300 100
***Try #2 on
your own!
The answer will always just be a number without units!
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
3x
B
***Remember,
perimeter is all sides
added together
5x
5x
3x + 5x + 3x + 5x = 32
x=2
D
C
3x
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.
3x
• Example:
x
2x
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
C
x + x + 2x = 180
4x = 180 Are we
x = 45 finished?
2x
A  45
B  45
C  90
A
x
x
B
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
2x
x
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
4
5
How can we
find the
missing
pieces?
Similar Figures
12 x 3 = 36
Label what we
know first!
15
12
How can we
find the missing
pieces?
5
15 ÷ 3 = 5
15
Does anyone know how to
find the missing piece?
If we go from big
12
13
to small we
multiply. From
small to big divide.
39
36
Proportions
equation
b and c
extreme
mean
a and d
mean
extreme
Proportions
extremes
means
So, ad = bc
reciprocals
b d
So, 
a c
Examples
8 1
• 1) 
x 2
• 2)
5
1

y4 y
10
4
• 3) 
4x x 1
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?’s
1. 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 ?’s
2. 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 ?’s
4. 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 ?’s
5. 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