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SMCHS
Geometry B
Mr. Ricks
Chapter 7
Homework Assignments:
Section 7.1
Section 7.2
Section 7.3
Section 7.4
Section 7.5
Section 7.6
p. 243 – 244:
p. 246 – 247:
p. 250 – 251:
p. 256 – 257:
p. 264 – 266:
p. 271 – 272:
Chapter 7 Review:
Chapter 7 Extra Credit:
Review)
1 – 13 all (CE), 1 – 20 all (WE)
1 – 11 all (CE), 1 – 20 all (WE)
1 – 9 all (CE), 1 – 21 all (WE)
1 – 11 all (CE), 1- 13 all (WE)
1 – 6 all (CE), 1 – 10 all (WE)
1 – 9 all (CE), 1 – 11 all (WE)
p. 277 – 278: 1-24 all (Chapter review)
p. 279 – 280: 1-14 all (Chapter test), 1 – 29 odd (Algebra
Section 7-1: Ratio and Proportion
The ratio of one number to another is the quotient when the first number is divided by the
second. Ratios are used to compare two numbers. You must use the same units (cm, m,
yard, etc.) for the ratio to be accurate.
Examples:
4 to 1
4:1
4
1
These are all examples of a single ratio written different ways.
20 m and 65m. p.h are examples of ratio that measure rate of change, or speed. Since the
s
ratios use different units, miles vs. meters and seconds vs. hours, you cannot accurately
compare the ratios.
A proportion is an equation stating that two ratios are equal.
Examples:
1 9

is an example of a proportion. In this case, you have true statement.
3 27
Section 7-2: Properties of Proportions
We can cross multiply proportions. This allows us to solve for a missing number in a
proportion using the other three.
4 x

3 12
3 x  412
10 4

n 9
4n  910
3 x  48
4n  90
x  16
n  22.5
Section 7-3: Similar Polygons
Two polygons are similar if their vertices can be paired so that:
a) Corresponding angles are congruent
b) Corresponding sides are in proportion (their lengths have the same ratio)
F
G
B
C
E
A
D
m AB = 3.00 cm
H
m EF = 4.25 cm
ABCD is a sqaure. EFGH is a square.
ABCD is similar to EFGH (written as ABCD  EFGH)
because:
1) the corresponding angles are congruent.
2) the corresponding sides are in proportion.
What is the scale factor for the above picture? _____
If two polygons are similar, then the ratio of the lengths of two corresponding sides is
called the scale factor of the similarity.
J
M
L
N
I
K
m JI = 5.00 cm
IJK and
IJK and
IJK and
because:
m M L = 2.50 cm
LMN are equilateral triangles.
LMN are also __________ triangles.
LMN are similar triangles (written as
IJK 
LMN)
1) the corresponding angles are congruent.
2) the corresponding sides are in proportion.
What is the scale factor for the above picture? _____
Section 7-4: A Postulate for Similar Triangles
Postulate 15: AA Similarity Postulate
If two angles of one triangle are congruent to two angles of another triangle, then the
triangles are similar.
O
P
mOQP = 60.00
S
mQPO = 60.00
mSRT = 60.00
R
mRTS = 60.00
Q
T
Since
OPQ and
STR both have two angles who measure 60,
we can say these triangles are similar by the AA Similarity Theorem.
This theorem allows us to say this without any more information,
simply having two pairs of congruent angles is enough to say the triangles are similar.
Using symbols,
OPQ 
STR.
Section 7-5: Theorems for Similar Triangles
Theorem 7-1: SAS Similarity THM
If an angle of one triangle is congruent to an angle of another triangle and the sides
including those angles are in proportion, then the triangles are similar.
X
V
mUVA = 30.00
mWXY = 30.00
A
U
Y
m VA = 2.50 cm
m VA
m XY = 7.45 cm
m XY
= 0.34
m VU = 2.16 cm
m VU
m XW = 6.45 cm
m XW
= 0.34
W
Since m UVA   WXY and the scale factor that compares VA and XY
as well as VU and XW are the same, we can say
WXY 
UVA.
Theorem 7-2: SSS Similarity THM
If the sides of two triangles are in proportion, then the triangles are similar.
Section 7-6: Proportional Lengths
Theorem 7-3: Triangle Proportionality THM
If a line parallel to one side of a triangle intersects the other two sides, it divides those
sides proportionally.
Corollary:
If three parallel lines intersect two transversals, then they divide the transversals
proportionally
Theorem 7-4: Triangle Angle-Bisector THM
If a ray bisects an angle of a triangle, then it divides the opposite side into segments
proportional to the other two sides.