Transcript Day 4 – Similar Figures

Warm-Up
SILENTLY…
1. Get out a blank sheet of
paper, and a pencil.
2. Wait quietly for further
instructions.
Thinking Maps are visual tools for learning, and include eight visual
patterns each linked to a specific cognitive process. Each
diagram type is intended to correspond with eight different
fundamental thinking processes. They are supposed to provide a
common visual language to information structure, often
employed when students take notes.
Circle Map
used for defining in context
Bubble Map
used for describing with adjectives
Flow Map
used for sequencing and ordering events
Brace Map
used for identifying part/whole relationships
Tree Map
used for classifying or grouping
Double Bubble Map
used for comparing and contrasting
Multi-flow map
used for analyzing causes and effects
Bridge map
used for illustrating analogies
CIRCLE MAP
Thinking Skill: Defining in Context & Brainstorming
How do
you know
this?
Ideas,
examples,
definition
How do
you know
this?
Ideas,
examples,
definition
Main
Idea or
Concept
Ideas,
examples,
definition
How do
you know
this?
Ideas,
examples,
definition
How do
you know
this?
On your paper, create your circle map.
Unit 1
Unit 1: Transformations, Congruence, and Similarity
Standards:
• MCC8.G.1 Verify experimentally the properties of rotations, reflections, and
translations: a. Lines are taken to lines, and line segments to line segments of
the same length. b. Angles are taken to angles of the same measure. c.
Parallel lines are taken to parallel lines.
• MCC8.G.2 Understand that a two‐dimensional figure is congruent to another
if the second can be obtained from the first by a sequence of rotations,
reflections, and translations; given two congruent figures, describe a
sequence that exhibits the congruence between them.
• MCC8.G.3 Describe the effect of dilations, translations, rotations, and
reflections on two‐dimensional figures using coordinates.
• MCC8.G.4 Understand that a two‐dimensional figure is similar to another if the
second can be obtained from the first by a sequence of rotations, reflections,
translations, and dilations; given two similar two‐dimensional figures, describe
a sequence that exhibits the similarity between them.
• MCC8.G.5 Use informal arguments to establish facts about the angle sum and
exterior angle of triangles, about the angles created when parallel lines are
cut by a transversal, and the angle‐angle criterion for similarity of triangles.
Math 8
Day 4
Learning Target:
Students can set up proportions for similar
figures and solve for the missing side.
Similar Figures
Goal 1
Identify Similar Polygons
Goal 2
Find the missing value
Goal 3
Describe a sequence that
exhibits the similarity between
two similar two‐dimensional figures
Similar polygons are polygons for which
all corresponding angles are congruent
and all corresponding sides are
proportional.
Example:
Similar Polygons
Polygons are said to be similar if :
a) there exists a one to one correspondence
between their sides and angles.
b) the corresponding angles are congruent
and
c) their corresponding sides are proportional
in lengths.
Definition of Similar Polygons -
Two polygons are SIMILAR if and only if their
corresponding angles are congruent and the
measures of their corresponding sides are
proportional.
In the diagram,
pentagon GHIJK is
similar to (~)
pentagon ABCDE, if
all corresponding
sides are proportional
GHIJK ~ ABCDE
G
H
A
B
C
E
K
I
J
G H HI
IJ
JK KG




AB BC CD DE EA
D
Example 1
Find the value of x, y, and the
measure of P if TSV ~ QPR.
x=6
y = 10.5
P = 86°
Example 2
Trapezoid ABCD is similar to trapezoid PQRS. List all the pairs of
congruent angles, and write the ratios of the corresponding sides in
a statement of proportionality.
A
D
P
B
S
Q
R
C
A  P, B  Q, C  R, D  P
AB BC CD AD



PQ QR RS PS
Example 3
Decide if the triangles
are similar.
M
10.5
P
4
18
L
Q
12
9
12
The triangles are not
similar.
R
N
Example 4
You have a picture that is 4 inches wide by 6
inches long. You want to reduce it in size to fit a
frame that is 1.5 inches wide. How long will the
reduced photo be?
Width 4 1.5
 
length 6 x
width  2.25 inches
Sequences That Exhibit Similarity
• You can use sequences of translations,
reflections, rotations, and dilations to
determine if 2 figures are similar.
• Meaning, look at the 2 figures. If you were
to slide, flip, rotate, enlarge, or shrink the
first figure, would it then be congruent to
the second figure?
Scale factor: The ratio of the lengths of two
corresponding sides of similar polygons
/ A  / E;
/ B  / F; / C  / G;
/D/H
AB/EF = BC/FG= CD/GH = AD/EH
The scale factor of polygon ABCD to polygon
EFGH is 10/20 or 1/2
In figure, there are two similar triangles .  LMN and
 PQR.
8
7
10


 1 .33
6 5 .25 7 .5
This ratio is called the scale factor.
Perimeter of  LMN = 8 + 7 + 10 = 25
Perimeter of  PQR = 6 + 5.25 + 7.5 = 18.75
Theorem 8.1
If two polygons are similar, then the
ratio of their perimeters is equal to the
ratios of their corresponding sides.
B
C
P
A
D
S
If ABCD ~ SPQR,
then
Q
R
AB  BC  CD  AD AB BC CD AD




SP  PQ  QR  RS
SP PQ QR SR
Find the Missing Value
• To find the missing value, set up a
proportion, cross multiply, then divide to
find the missing value.
Example 5
Parallelogram GIHF is similar to
parallelogram LKJF. Find the value of y.
F
J
Y = 19.2
12
L
15
H
K
y
G
24
I
Example 6: The triangles CAT and DOG are similar. The larger triangle is an
enlargement of the smaller triangle. How long is side GO?
T
G
2 cm
1.5 cm
? cm
A
3 cm
O
C
3 cm
6 cm
D
Each side and its enlargement
form a pair of sides called
corresponding sides.
(1) Corresponding side of TC -->
GD
(2) Corresponding side of CA-->
DO
(3) Corresponding side of TA-->
GO
Length of
corresponding
sides
GD=3
TC=1.5
DO=6
CA=3
GO=?
TA=2
Ratio of Lengths
3/1.5=2
6/3=2
?/2=2
The scale factor is 2.
G
? cm
T
2 cm
3 cm
1.5 cm
O
A
C
3 cm
D
6 cm
(1) Each side in the larger triangle is twice the size of
the corresponding side in the smaller triangle.
(2) Now, let’s find the length of side GO
i) What side is corresponding side of GO? TA
ii) What is the scale factor?
2
iii) Therefore, GO= scale factor x TA
iv) So, GO= 2 x 2 = 4 cm
What did we just learn about
similar polygons ?
Equal angles
Different size
Same shape
Similar polygons
Corresponding side
Size-change factor
Example 1: Quadrangles ABCD and EFGH are similar.
How long is side AD? How long is side GH?
12÷ 4= 3 & 18÷ 6=3
(1) What is the scale factor?
(2) What is the corresponding
side of AD ? EH
H
(3) How long is side AD? AD = 5
15 cm
(4) What is the corresponding
side of GH? CD
(5) How long is side GH?
7 x 3 = GH, GH = 21
?cm
E
? cm
D
12cm
A
7cm
4cm
C
B
F
6cm
18 cm
G
Example 2 : Figure MORE is similar to Figure SALT. Select the right
answer with the one of the given values below.
(1) The length of segment TL is
a. 6 cm b. 6.5 cm c. 7 cm d. 7.5 cm
(2) ER corresponds to this segment. E
a. TS b. TL c. AL d. SA
M
O
R
A
S
(3) EM corresponds to this segment.
a. TS b. TL c. SA d. AL
(4) The length of segment MO.
T
a. 6 cm b. 6.5 cm c. 7 cm d. 7.5 cm
L