Transcript Powerpoint - mathplease.com

Let’s grade homework
Pg 138 – 143; 5-9, 17-21, not 8c
3.1.3 - Proportional Equations
3.1.4 – Using Proportional
equations
Ratio
Proportion
A comparison of 2 things.
An equation where 2 ratios
are equal to each other
Can be written like:
Written like:
Dogs : cats (in words)
2:1
(with a colon)
(3 + x) = 5
7
2
3
4
(as a fraction)
Use cross products to solve.
How are ratios and proportions the
same?
How are they different?
I will number each row.
Back person: please get the appropriate paper from the back table
– one paper for each person – and hand them out.
Second person from the back: please get a straightedge for
everyone in your row.
Everyone: please follow the instructions on the paper and
complete your paper independently.
In 5 minutes, you will be able to compare your answers to others in
your row to come up with a final solution.
Then, make a table and come up with some conjectures..
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#1
Put a point of dilation somewhere inside
the shape.
Measure the sides of your shape in cm.
Dilate the shape by a scale factor of 2.
Find the perimeter of the pre-image.
Find the perimeter of the image.
Find the area of the pre-image.
Find the area of the image.
#2
#4
#3
#5
shape 1
perimeter of pre-image
perimeter of image
area of pre-image
area of image
shape 2
shape 3
shape 4
shape 5
Naming & Comparing Polygons
♥ List vertices in order, either
clockwise or counterclockwise.
♥ When comparing 2 polygons,
begin at corresponding vertices;
name the vertices in order and; go
in the same direction.
♥ By doing this you can identify
corresponding parts.
D
E
C
A
B
DCBAE
I
H
J
P
 D corresponds to I
AE corresponds to PH
K
IJKPH
Name corresponding parts
• Name all the angles that correspond:
I
D corresponds to  I
 C corresponds to  J E
 B corresponds to  K
 A corresponds to  P A
 E corresponds to  H
D
H
C
J
B
P
DCBAE
IJKPH
K
• Name all the segments that correspond:
DC corresponds to IJ
CB corresponds to JK
BA corresponds to KP
AE corresponds to PH
ED corresponds to HI
How many
corresponding
angles are
there?
5
How many
corresponding
sides are there?
5
D
E
C
A
• How many ways
can you name
pentagon DCBAE?
10
B
Do it.
Pick a vertex and go clockwise
Pick a vertex and go counterclockwise
DCBAE
DEABC
CBAED
CDEAB
BAEDC
BCDEA
AEDCB
ABCDE
EDCBA
EABCD
Similarity Statements
• Given: These polygons
are similar.
A
E
B
F
• Remember, if they are
SIMILAR, corresponding
sides have the same
RATIO.
D
C
AB ~ EF
H
DA ~ HE
DC ~ HG
CB ~ GF
G
ABCD ~ EFGH
Corresponding
angles in a
similar figure
are congruent!!
Corresponding angles in a similar
figure are congruent
A
E
B
D
C
H
G
F
A ~= E
B ~= F
D ~= H
C ~= G
Quick check
How many different ways can you name ΔABC?
What is the relationship of corresponding sides in a similar figure?
What is the relationship of corresponding angles in a similar figure?
What happens to the perimeter of a shape that has been dilated by a scale factor of
2?
What happens to the area of a shape that has been dilated by a scale factor of 2?
What is the simplified, exact answer to: √3 + 5√3 ?
What is the name of angle pair c and h?
Are angles c and h congruent, supplementary or neither? Defend your answer.
What is the name of angle pair b and g?
What is the measurement relationship between b and g? Defend your answer.
What is the sum of the angles in a triangle?
What is the sum of the angles in a quadrilateral?
If a shape has a scale factor of 3, is the pre-image larger or smaller than the image?
e
a
b
f
c
h
d
g
Your
assignment
Pg 146 – 151;
27-31, 38-42