welcome to class. please pick up a warm up off the table
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Welcome to class. Please pick up a warm up off the table. and do it!. Let’s grade homework. Pg 138 – 143; 5-9, 17-21, not 8c. 3.1.3 - Proportional Equations 3.1.4 – Using Proportional equations. A comparison of 2 things. Can be written like: Dogs : cats (in words) - PowerPoint PPT PresentationTRANSCRIPT
Let’s grade homework
Pg 138 – 143; 5-9, 17-21, not 8c
3.1.3 - Proportional Equations3.1.4 – Using Proportional
equations
Ratio
A comparison of 2 things.
Can be written like:
Dogs : cats (in words)
2:1 (with a colon)
3 (as a fraction)4
An equation where 2 ratios are equal to each other
Written like:
(3 + x) = 5
7 2
Use cross products to solve.
Proportion
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..
• 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.
#4
#2
#3
#1
#5
shape 1 shape 2 shape 3 shape 4 shape 5
perimeter of pre-image
perimeter of image
area of pre-image
area of image
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.
A
D
C
B
E
DCBAE
P
I
J
K
H
IJKPH
D corresponds to I
AE corresponds to PH
Name corresponding parts
• Name all the angles that correspond:
A
D
C
B
E
P
I
J
K
H
D corresponds to I C corresponds to J B corresponds to K A corresponds to P E corresponds to H
DCBAE IJKPH
• Name all the segments that correspond:DC corresponds to IJCB corresponds to JKBA corresponds to KPAE corresponds to PHED corresponds to HI
How many corresponding
angles are there?
How many corresponding
sides are there?
5 5
• How many ways can you name pentagon DCBAE?
A
D
C
B
E
10
Do it.
DCBAE
CBAED
BAEDC
AEDCB
EDCBA
Pick a vertex and go clockwise Pick a vertex and go counterclockwise
DEABC
CDEAB
BCDEA
ABCDE
EABCD
Similarity Statements• Given: These polygons
are similar.
• Remember, if they are SIMILAR, corresponding sides have the same RATIO.
G
H
FE
C
D
BA
ABCD ~ EFGH
AB ~ EF
DA ~ HE
DC ~ HG
CB ~ GF
SIMILARITY STATEMENTS
SIMILARITY STATEMENT
Corresponding angles in a similar figure are congruent!!
Corresponding angles in a similar figure are congruent
A EB FD HC GC
D
BA
G
H
FE
=~
=~=~=~
Quick checkHow 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?
a
dbh g
ec
f
Your assignment
Pg 146 – 151;
27-31, 38-42