Geometry
Unit 6
Proportions and Similarity
Name:________________________________________________
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Geometry
Chapter 6 – Proportions and Similarity
***In order to get full credit for your assignments they must me done on time and you must SHOW ALL
WORK. ***
1.____ (6-1) Proportions. Page 285 – 286 # 12 – 22, 25, 28 – 34 even
2. ____ (6-2) Similar Polygons Page 293 – 294 # 11 – 20, 27 – 33, 34 – 38 even
3. ____ (6-3) Similar Triangles – Day 1 Page 301 # 10 – 21, 41, 42
4. ____ (6-3) Similar Triangles – Day 2 – 6-3 Practice Worksheet or Page 301 # 1 – 9
5. ____ (6-4) Parallel Lines and Proportional Parts – Day 1– Page 312 # 14 – 26, 33, 34
6.____ (6-4) Parallel Lines and Proportional Parts – Day 2 - 6-4 Practice Worksheet or Page 311
# 1 – 13
7. _____ (6-5) Parts of Similar Triangles – Day 1 - Page 320 # 10-15, 18-27
8. _____(6-5) Parts of Similar Triangles – Day 2 - 6-5 Practice Worksheet or Page 319 #1 – 7, 9
9. _____ Unit 6 Review Worksheet
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Date: _________________________
Section 6 – 1: Proportions
Notes
Write Ratios:
Ratio:
Ways to express the ratio a to b:
Example #1: The total number of students who participate in sports programs at
Woodland Hills High School is 703. The total number of students in the school is 1850.
Find the athlete-to-student ratio to the nearest tenth.
Extended Ratios in Triangles:
Example #2: In a triangle, the ratio of the measures of three sides is 5:12:13, and the
perimeter is 90 centimeters. Find the measure of the shortest side of the triangle.
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Properties of Proportions:
Proportion:
Cross Products:
Extremes:
Means:
Example #3: Solve each proportion.
a.)
3 x

5 75
b.)
3x  5  13

4
2
c.)
2 .3
y

4
3 .4
Example #4: A boxcar on a train has a length of 40 feet and a width of 9 feet. A scale
model is made with a length of 16 inches. Find the width of the model.
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CRITICAL THINKING
Graph polygon ABCD and MN . Find the
coordinates for vertices L and P such that
ABCD ~ NLPM.
A (2, 0), B (4,4), C (0, 4), D (-2, 0);
M(4, 0), N (12,0)
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Date: _________________________
Section 6 – 2: Similar Polygons
Notes
IDENTIFY SIMILAR FIGURES
Similar Polygons:
Key Concept – Two polygons are _______________if and only if their corresponding
_____________ are congruent and the measures of their corresponding sides are
____________________.
Symbol:
Example:
Similarity statement:
Congruent angles:
Corresponding sides:
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Example #1: Determine whether the pair of figures is similar. Justify your answer.
Scale Factor – a numerical ________ when comparing the lengths of corresponding
___________ of similar figures
Example #2: Some special effects in movies are created using miniature models. In a
recent movie, a model SUV 22 inches long was created to look like a real 14 2/3-foot
SUV. What is the scale factor of the model compared to the real SUV?
Example #3: The two polygons are similar.
(a) Write a similarity statement.
(b) Find x, y, and UV.
(c) Find the scale factor of polygon ABCDE to polygon RSTUV.
a.)
b.)
c.)
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CRITICAL THINKING
Photography:
Joe reduced a photograph that is 21.3 centimeters by 27.5 centimeters so that it
would fit in a 10-centimeter by 10-centimeter frame.
a) Find the maximum dimensions of the reduced photograph.
b) What percent of the original length is the length of the reduced photograph?
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Date: _____________________________
Section 6 – 3: Similar Triangles
Notes
IDENTIFY SIMILAR TRIANGLES
Angle-Angle (AA) Similarity:
If the two ______________ of one triangle are
___________________ to two angles of another triangle, then the triangles are
___________________.
Example:
Side-Side-Side (SSS) Similarity: If the measures of the corresponding ___________ of
two triangles are _______________________, then the triangles are similar.
Example:
Side-Angle-Side (SAS) Similarity: If the measures of two ____________ of a triangle
are proportional to the measures of two corresponding sides of another triangle and
the included ____________ are congruent, then the triangles are ___________________.
Example:
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Example #1: In the figure, FG  EG , BE = 15, AE = 9, and DF = 12, CF = 20. Determine
which triangles in the figure are similar.
Example #2: Given RS ‖ TU , RS = 4, RQ = x + 3, QT = 2x + 10, UT = 10, find RQ and QT.
Example #3: Josh wanted to measure the height of the Sears Tower in Chicago. He
used a 12-foot light pole and measured its shadow at 1 pm. The length of the shadow
was 2 feet. Then he measured the length of the Sears Tower’s shadow and it was 242
feet at that time. What is the height of the Sears Tower?
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CRITICAL THINKING
The coordinates of RST are R (-10, 6), S (-2, 4),
and T (-4, -2). Point D (6, 2) lies on RS .
Graph the triangle and point D and draw SD .

Where should a point E be located so that
RST~ RDE ?
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Date: _____________________________
Section 6 – 4: Parallel Lines and Proportional Parts
Notes
PROPORTIONAL PARTS OF TRIANGLES
Triangle Proportionality Theorem: If a line is __________________ to one side of a
triangle and intersects the other two sides in two distinct points, then it separates these
sides into segments of ______________________ lengths.
Example:
Example #1: In ∆RST, RT ║ VU , SV = 3, VR = 8, and UT = 12. Find SU.
Converse of the Triangle Proportionality Theorem: If a line intersects two sides of a
________________ and separates the sides into corresponding segments of proportional
______________, then the line is _________________ to the third side.
Example:
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Example #2: In ∆DEF, DH = 18, HE = 36, and DG = ½ GF. Determine whether GH ║ FE .
Explain!
Triangle Midsegment Theorem: A midsegment of a triangle is ______________ to one
side of the triangle, and its length is _________________ the length of that side.
Example:
Example #3: In the figure, OA is a midsegment of ∆MTH. Find x and y.
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CRITICAL THINKING
Construction:
Two poles, 30 feet and 50 feet tall, are 40 feet
apart and perpendicular to the ground. The
poles are supported by wires attached from
the top of each pole to the bottom of the
other, as in the figure. A coupling is places at
where the two wires cross.
1) Find x, the distance from C to the taller pole.
2) How high above the ground is the coupling?
3) How far down the wire from the smaller pole is the coupling?
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C
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Date: ______________________
Section 6 – 5: Parts of Similar Triangles
Notes
PERIMETERS
Perimeter:
Theorem 6.7: Proportional Perimeters Theorem – If two triangles are similar, then the
___________________
are
proportional
to
the
measures
of
the
________________________ sides.
Example: If LMN ~ QRS , QR  35, RS  37, SQ  12 , and NL  5 , find
the perimeter of LMN .
Theorem 6.8:
If two triangles are similar, then the _______________ of the
corresponding _________________ are proportional to the measures of the
corresponding sides.
Example:
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Theorem 6.9: If two triangles are similar, then the measures of the corresponding
_____________
_________________ are proportional to the measures of the
corresponding sides.
Example:
Theorem 6.10: If two triangles are similar, then the measures of the corresponding
_________________ are proportional to the measures of the corresponding sides.
Example:
Example #1: Draw ABC ~ DEF . BG is a median of ABC , and EH is a median of DEF
. Find EH if BC = 30, BG = 15, and EF = 15.
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CRITICAL THINKING
1. A triangular track is laid out as shown. RST~
WVU . If UV = 500 feet, VW = 400 feet, UW = 300
feet, and ST = 1000 feet, find the perimeter of

RST.

2. ART: Use the diagram of a square mosaic tile.
AB = BC = CD = 1/3AD and DE = EF = FG = 1/3 DG.
a) What is the ratio of the perimeter of BDF to the
perimeter of BCI ? Explain.
b) Find two triangles such that the ratio of their perimeters is 2:3. Explain.
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