Download Ratios and Proportions - Trimble County Schools

7-1
Ratios and Proportions
Vocabulary
Review
1. Write a ratio to compare 9 red marbles to 16 blue marbles in three ways.
9
9 to 16
9 : 16
16
In simplest form, write the ratio of vowels to consonants in each word below.
2. comparison
3. geometry
2
4. ratio
1 to 1
3
: 2
3
5. Cross out the ratio that is NOT equivalent to 12 to 8.
6:2
24
16
9 to 6
48 : 32
A proportion always
includes an
equal sign, ä.
proportion (noun) pruh PAWR shun
Other Word Form: proportional (adjective)
Definition: A proportion is an equation stating that two ratios are equal.
8
5
Examples: 23 5 12 and 12 5 10 are proportions.
Use Your Vocabulary
6. Write 3 or 6 to make each proportion true.
2
35
6
9
3
4
6
58
1
35
2
5
6
3
10
5 6
Underline the correct word to complete each sentence.
7. Distance on a map is proportion / proportional to the actual distance.
8. The number of ounces in 3 lb is in proportion / proportional to the number
of ounces in 1 lb.
Chapter 7
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Vocabulary Builder
Key Concept Properties of Proportions
a
c
Cross Products Property In a proportion b 5 d , where b 2 0 and d 2 0, the
product of the extremes a and d equals the product of the means b and c.
a
c
5d
b
a?d5b?
c
ad 5 bc
Equivalent Forms of Proportions
Property 1
Property 2
Property 3
a
c
5 d is equivalent to
b
a
c
5 d is equivalent to
b
a
c
5 d is equivalent to
b
d
b
a5 c.
a
b
c 5 d.
a1b
c1d
5
.
b
d
9. Identify the means and extremes in the proportion 23 5 4x .
Means
3 and 4
Extremes
2 and x
Identify the Property of Proportions each statement illustrates.
3
3
10. If 12 5 14 , then 1 5 12
4 .
Property 2
8
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11. If 45 5 10 , then 4(10) 5 5(8).
Cross Products Property
3
3
9
Property 1
x
7
x1y
y .
Property 3
12. If 13 5 9 , then 1 5 3 .
3
13. If 4 5 y , then 4 5
Problem 1 Writing a Ratio
Got It? A bonsai tree is 18 in. wide and stands 2 ft tall. What is the ratio of the width
of the bonsai to its height?
14. The bonsai is 18 in. wide and 24 in. tall.
15. Write the same ratio three different ways.
width of bonsai to height of bonsai
Write using the
Write as a fraction.
Write using a colon.
word “to.”
18
18 : 24
18 to 24
24
183
Lesson 7-1
Using an Extended Ratio
Problem 3
Got It? The lengths of the sides of a triangle are in the extended ratio 4 : 7 : 9.
The perimeter is 60 cm. What are the lengths of the sides?
7Ƃ x
4x
16. Label the triangle at the right. Use the extended ratio to write
an expression for each side length.
9Ƃ x
17. Complete the model to write an equation.
Relate
the sum of the
side lengths
Write
4x à 7x à 9x
perimeter â
is the perimeter
â
60
60
18. Use the justifications below to find the value of x.
4x 1
x
1 9x 5 60
Write the equation.
20 ? x 5 60
Combine like terms.
20 ? x
5
20
x5
60
Divide each side by 20 .
20
3
Simplify.
19. Use the value of x to find each side length.
3
5 12
7 x
57?
9x 5
3
5 21
9
Problem 4 Solving a Proportion
a
?
Got It? Algebra What is the solution of the proportion 92 5 14
21. Write a justification for each statement below.
9(14) 5 2a
Chapter 7
Write a proportion.
Cross Products Property
126 5 2a
Multiply.
126
2a
2 5 2
Divide each side by 2.
a 5 63
3
5 27
20. The lengths of the sides of the triangle are 12 cm, 21 cm, and 27 cm.
9
a
2 5 14
?
Simplify.
184
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4x 5 4 ?
Problem 5
Writing Equivalent Proportions
y
Got It? Use the proportion 6x 5 7 . What ratio completes the equivalent
proportion 6x 5 j
j ? Justify your answer.
y
x
ã
6 7
22. Use the diagram at the right. Draw arrows from the x and the 6 in
the original proportion to the x and the 6 in the new proportion.
a
c
23. Circle the proportion equivalent to b 5 d that you can use.
d
b
a5 c
a1b
c1d
5 d
b
a
b
c 5d
x
y
6
xã
7
6
24. Complete: 6 5 7 is equivalent to x 5
.
y
Lesson Check • Do you UNDERSTAND?
Error Analysis What is the error in the solution of the proportion at the right?
7
3
25. Circle the means of the proportion. Then underline the extremes.
3
4
7
x
26. Write each product.
Means
3
?
5
4
Extremes
12
7
?
x
5
= 4x
28 = 3x
28
3
= x
7x
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27. What is the error in the solution of the proportion? Answers may vary. Sample:
The cross products are 7x and 12, not 28 and 3x.
_______________________________________________________________________
28. Now solve the proportion correctly.
7
3
5 x4
7x 5 12
x 5 12
7
Math Success
Check off the vocabulary words that you understand.
proportion
means
extremes
Cross Products Property
Rate how well you can solve proportions.
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review
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4
6
8
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get it!
10
185
Lesson 7-1
7-2
Similar Polygons
Vocabulary
Review
1. What does it mean when two segments are congruent?
They have the same length.
_______________________________________________________________________
2. What does it mean when two angles are congruent?
They have the same measure.
_______________________________________________________________________
3. Measure each segment. Then circle the congruent segments.
similar (adjective)
SIM
The symbol for
similar is
ƭ.
uh lur
Other Word Forms: similarity (noun), similarly (adverb)
Definition: Things that are similar are alike, but not identical.
Math Usage: Figures that have the same shape but not necessarily the same
size are similar.
Use Your Vocabulary Answers may vary. Samples are given.
4. How are the two squares at the right similar?
They have the same shape.
______________________________________________________
5. How are the two squares NOT similar?
They are not the same size.
______________________________________________________
Chapter 7
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Vocabulary Builder
Key Concept Similar Polygons
Two polygons are similar polygons if corresponding angles are congruent and if the
lengths of corresponding sides are proportional.
ABCD , GHIJ . Draw a line from each angle in Column A to its corresponding
angle in Column B.
Column A
Column B
6. /A
/H
7. /B
/J
8. /C
/G
9. /D
/I
I
H
C
B
D
A
J
G
10. Complete the extended proportion to show that
corresponding sides of ABCD and GHIJ are proportional.
CD
BC
AD
AB
5
5
GH 5
IJ
HI
GJ
Problem 1 Understanding Similarity
Got It? DEFG , HJKL. What are the pairs of congruent angles? What is the
extended proportion for the ratios of the lengths of corresponding sides?
11. Complete each congruence statement.
12. Complete the extended proportion.
/D > / H
EF
DE
HJ 5
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/E > / J
JK
5
FG
KL
5
DG
HL
/K > / F
/L > / G
A scale factor is the ratio of the lengths of corresponding sides of similar triangles.
Problem 2 Determining Similarity
Got It? Are the polygons similar? If they are, write a similarity
K 10 L
W
20
X
statement and give the scale factor.
15
15
13. Circle the short sides of each rectangle. Underline the long sides.
M
N
KL
LM
WX
Z
Y
NK
MN
XY
ZW
YZ
14. Write the ratios of corresponding sides in simplest form.
10
KL
XY 5 15 5
2
3
LM
YZ
5
15
20
5
3
4
10
MN
ZW 5 15 5
187
2
3
NK
WX 5
15
20
5
3
4
Lesson 7-2
15. Place a ✓ in the box if the statement is correct. Place an ✗ if it is incorrect.
✘
KLMN , XYZW and the scale factor is 23 .
✘
KLMN , XYZW and the scale factor is 4 .
✔
The polygons are not similar.
3
Problem 3 Using Similar Polygons
Got It? ABCD , EFGD. What is the value of y?
BC
CD
AB
y
AD
D
Corresponding sides of similar polygons are proportional.
6
Substitute.
9y 5 30
y 5 313
x
G
7.5
C
Divide each side by 9.
Got It? A rectangular poster’s design is 6 in. high by 10 in. wide. What are the
dimensions of the largest complete poster that will fit in a space 3 ft high by 4 ft wide?
18. Determine how many times the design can be enlarged.
Height: 3 ft 5 36 in.
Width: 4 ft 5 48 in.
36 in. 4 6 in. 5 6
48 in. 4 10 in. 5 4.8
The design can be enlarged at most 4.8 times.
19. Let x represent the height of the poster. Write a proportion and solve for x.
5 x6
10x 5 288
x 5 28.8
20. The largest complete poster that will fit is
Chapter 7
B
Cross Products Property
Problem 4 Using Similarity
10
48
F
ED
5 AD
59
5
y
6
17. Use the justifications at the right to find the value of y.
EF
E
5
28.8
in. by 48 in.
188
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AB
9
16. Circle the side of ABCD that corresponds to EF .
A
Problem 5
Using a Scale Drawing
Got It? Use the scale drawing of the bridge. What is the actual height of the
towers above the roadway?
0.8
21. Use a centimeter ruler to
measure the height of the
towers above the roadway
in the scale drawing.
Label the drawing with
the height.
cm Scale 1 cm : 200 m
22. Identify the variable.
Let h 5 the 9 of the towers.
actual height
23. Use the information on the scale drawing to write a proportion. Then solve to find
the value of the variable.
1 5 tower height in drawing (cm) R
Q Hint:
actual height (m)
200
1
200
5 0.8
h
h 5 160
24. The actual height of the towers above the roadway is 160 m.
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Lesson Check • Do you UNDERSTAND?
B
The triangles at the right are similar. What are three similarity statements
for the triangles?
25. The triangles are n
26. /A > / P
ABS
and n
/B > / R
PRS
S
/S > / S
nBSA , kRSP
27. nABS , kPRS
P
.
nSAB , kSPR
A
R
Math Success
Check off the vocabulary words that you understand.
similar
extended proportion
scale factor
scale drawing
Rate how well you can identify and apply similar polygons.
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review
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get it!
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189
Lesson 7-2
7-3
Proving Triangles
Similar
Vocabulary
Review
Write the converse of each theorem.
1. If the diagonals of a parallelogram are perpendicular, then the parallelogram
is a rhombus.
a parallelogram is a rhombus
If
then
,
its diagonals are perpendicular
.
If
then
a point is equidistant from the endpoints of a segment
,
it is on the perpendicular bisector of the segment
.
Vocabulary Builder
verify (verb)
VEHR
uh fy
Related Word: proof (noun)
Definition: To verify something means to find the truth or accuracy of it.
Math Usage: A proof is a way to verify a conjecture or statement.
Use Your Vocabulary
Write T for true or F for false.
F
3. You can verify that two triangles are similar by showing that corresponding
angles are proportional.
T
4. You can use properties, postulates, and previously proven theorems to verify
steps in a proof.
Chapter 7
190
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2. If a point is on the perpendicular bisector of a segment, then it is equidistant from
the endpoints of the segment.
Key Concept
Postulate 7–1, Theorem 7–1, Theorem 7–2
Postulate 7-1 Angle-Angle Similarity (AA ,) Postulate If two angles of
one triangle are congruent to two angles of another triangle, then the
triangles are similar.
Theorem 7-1 Side-Angle-Side Similarity (SAS ,) Theorem If an angle of one
triangle is congruent to an angle of a second triangle, and the sides that include the
two angles are proportional, then the triangles are similar.
Theorem 7-2 Side-Side-Side Similarity (SSS ,) Theorem If the corresponding
sides of two triangles are proportional, then the triangles are similar.
5. Write the postulate or theorem that proves the triangles similar.
4
2
3
6
SAS , Theorem
Problem 1 Using the AA , Postulate
Got It? Are the two triangles similar? How do you know?
39í
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6. Complete the diagram.
39î
7. Are the triangles similar? Explain. Explanations may vary.
51î
Sample:
Yes. Three pairs of corresponding angles are
_________________________________________________________
51í
congruent, so the triangles are similar by the AA , Postulate.
__________________________________________________________
Problem 2
Verifying Triangle Similarity
Got It? Are the triangles similar? If so, write a similarity statement
9
A
for the triangles and explain how you know the triangles are similar.
6
8. Write ratios for each pair of corresponding sides.
AB
EF
9
5 12
5 34
AC
EG
5 68 5 34
BC
FG
C
G
B
8
6
E
8
12
F
5 68 5 34
9. Circle the postulate or theorem you can use to verify that the triangles are similar.
AA , Postulate
SAS , Theorem
SSS , Theorem
10. Complete the similarity statement.
nABC ,n EFG
191
Lesson 7-3
Problem 3
Proving Triangles Similar
Got It? Given: AC uu MP
Prove: nABC , nPBM
P
C
11. The proof is shown below. Write a reason from the box for each statement.
A
AA ~ Postulate
B
M
Given
Vertical angles are
congruent.
Statements
Reasons
1) AC uu MP
1)
2) /A > /P
2) If parallel lines are cut by a transversal, alternate interior angles
are congruent.
3) /ABC > /PBM
3)
Vertical angles are congruent.
4) nABC , nPBM
4)
AA , Postulate
Given
Problem 4 Finding Lengths in Similar Triangles
Before rock climbing,
Darius wants to know
how high he will climb.
He places a mirror on
the ground and walks
backward until he can
see the top of the cliff in
the mirror.
J
x ft
H
5.5 ft
T
34 ft
6 ft V
S
12. If the ground is NOT flat, will /HTV and /JSV be right angles?
Yes / No
13. If the ground is NOT flat, will you be able to find congruent angles?
Yes / No
14. Why is it important that the ground be flat? Explain.
Answers may vary. Sample: If the ground is flat, lHTV and lJSV will
___________________________________________________________________
be right angles and lHVT and lJVS will be congruent.
___________________________________________________________________
Chapter 7
192
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Got It? Reasoning Why is it important that the ground be flat to use the method
of indirect measurement illustrated in the problem below? Explain.
Lesson Check • Do you UNDERSTAND?
Error Analysis Which solution for the value of x in the figure at the right is not
correct? Explain.
9
4
A.
4
8
B.
= 8x
8
x
4x = 72
x = 18
x
8
= 46
6
48 = 4x
12 = x
6
15. Write the side lengths of the triangles.
Triangle
Shortest Side
Longest Side
Third Side
Larger
6
x
9
Smaller
4
8
6
16. Write ratios to compare the lengths of the corresponding sides.
6
4
shortest sides:
longest sides:
x
8
third sides:
9
6
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17. Cross out the proportion that does NOT show ratios of corresponding sides.
9
6
654
9
x
6
x
8
58
x
9
54
8 5 6
18. Cross out the solution that does NOT show ratios of corresponding sides.
4
Solution A
Solution B
Explanations may
19. Explain why the solution you crossed out does NOT show the correct value of x. vary. Sample:
Solution A does not show ratios of corresponding sides.
_______________________________________________________________________
Math Success
Check off the vocabulary words that you understand.
indirect measurement
similar triangles
Rate how well you can prove triangles similar.
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review
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get it!
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193
Lesson 7-3
7-4
Similarity in Right
Triangles
Vocabulary
Review
Underline the correct word to complete the sentence.
1. The altitude of a triangle is a segment from a vertex to the opposite
side that is parallel / perpendicular to the opposite side.
C
2. In an isosceles triangle, the altitude to the base divides the triangle
into two congruent / isosceles triangles.
3. Circle the altitude of nABC.
AC
AB
BC
A
CD
D
B
Vocabulary Builder
Definition: For any two positive numbers a and b, the geometric mean of a and b is
a
x
the positive number x such that x 5 b .
x
Example: The geometric mean of 4 and 10 is the value of x in x4 5 10 , or
x 5 2"10.
Use Your Vocabulary
4. Multiple Choice Which proportion can you use to find the geometric mean
of 5 and 15?
x
x
5 5 15
5
15
x 5 x
5
x
x 5 15
5
x
15 5 x
Underline the correct equation to complete each sentence.
5. The geometric mean x of a and b is x 5 "ab / x 5 ab .
6. The geometric mean x of 3 and 7 is x 5 "21 / x 5 21 .
7. Circle the geometric mean of !3 and !3.
!3
Chapter 7
3 !3
3
194
!33
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geometric mean (noun) jee uh MEH trik meen
Key Concept Theorem 7-3 and Corollaries 1 and 2
Theorem 7-3 The altitude to the hypotenuse of a right triangle divides the triangle into
two triangles that are similar to the original triangle and to each other.
C
If . . .
nABC is a right triangle
with right /ACB, and
CD is the altitude to the
hypotenuse
A
D
D
D
A
Corollary 1 to Theorem 7-3
The length of the altitude to the
hypotenuse of a right triangle is the
geometric mean of the lengths of the
segments of the hypotenuse.
Corollary 2 to Theorem 7-3
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Then . . .
The altitude to the hypotenuse of a right
triangle separates the hypotenuse so that
the length of each leg of the triangle is
the geometric mean of the length of the
hypotenuse and the length of the segment
of the hypotenuse adjacent to the leg.
C
nABC , nACD
nABC , nCBD
B
nACD , nCBD
B
C
If . . .
Then . . .
C
A
CD
AD
CD 5 DB
B
D
If . . .
Then . . .
AC
AB
AC 5 AD
C
CB
AB
CB 5 DB
A
B
D
8. nLMN is a right triangle with right /LMN . NP is the altitude to
the hypotenuse. Complete the similarity statements.
N
L
nLMN , n LNP
P
nLMN , n NMP
M
nLNP , n NMP
Use the triangle at the right. Write Corollary 1 or Corollary 2 for each proportion.
c
a
9. a 5 x
Corollary 2
a
10. m 5 y
Corollary 1
c
Corollary 2
x
m
b
11. b 5 y
x
m
b
y
c
195
Lesson 7-4
Problem 1 Identifying Similar Triangles
Got It? What similarity statement can you write relating the
S
Q
three triangles in the diagram?
R
12. Write the names of the triangles.
nRPQ
n PQS
P
n PRS
13. Write the three right angles.
/RPQ
/ QSP
14. Write the three smallest angles.
/ PSR
/QRP
/ SPQ
/ SRP
15. Use your answers to Exercises 13 and 14 to write three similarity statements
beginning with the vertex of the smallest angle in each triangle and ending with
the vertex of the right angle.
nRQP , n
PQS
nRQP , n
n PQS
RPS
,n
RSP
Problem 2 Finding the Geometric Mean
Got It? What is the geometric mean of 4 and 18?
16. Use the justifications below to find the geometric mean.
x
4
Definition of geometric mean
x 5
18
x5
x5
72
Å
6
Cross Products Property
Take the positive square root of each side.
72
Å
Problem 3
Write in simplest radical form.
2
Using the Corollaries
4
Got It? What are the values of x and y?
Underline the correct word to complete each sentence.
17. x is the length of a leg of the largest
x
5
y
18. y is the length of the altitude of the largest
triangle, so use Corollary 1 / Corollary 2
to find the value of x.
triangle, so use Corollary 1 / Corollary 2
to find the value of y.
19. The values of x and y are found below. Write a justification for each step.
x
4
x 5415
x 2 5 36
4
Write a proportion.
y
y
55
y 2 5 20
Cross Products Property
x 5 "36
Take the positive square root.
y 5 "20
x56
Simplify.
y 5 2"5
Chapter 7
196
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x2 5
Problem 4 Finding a Distance
Got It? Points A, B, and C are located so that AB 5 20 in., and AB ' BC.
B
Point D is located on AC so that BD ' AC and DC 5 9 in. You program a
robot to move from A to D and to pick up a plastic bottle at D. From point D,
the robot must turn right and move to point B to put the bottle in a
recycling bin. How far does the robot travel from D to B?
x
C
9 in. D
20 in.
16 in.
A
20. Place a ✓ in the box if the statement is correct. Place an ✗ if it is incorrect.
✔ I know the length of the hypotenuse of nABC.
✔ I know the lengths of the segments of the hypotenuse of nABC.
✘ I know the length of the altitude of nABC.
✔ I can use Corollary 1 to solve the problem.
21. Find the length of BD.
9
x
x2
x
5 16
5 144
x 5 "144
x 5 12
22. The robot travels 12 in. from D to B.
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Lesson Check • Do you UNDERSTAND?
Vocabulary Identify the following in nRST .
R
P
23. The hypotenuse is RT .
S
24. The segments of the hypotenuse are RP and TP .
T
25. The segment of the hypotenuse adjacent to leg ST is TP .
Math Success
Check off the vocabulary words that you understand.
geometric mean
altitude
similarity
Rate how well you understand similar right triangles.
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review
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get it!
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197
Lesson 7-4
7-5
Proportions in Triangles
Vocabulary
Review
10
1. Circle the model that can form a proportion with 15 .
2. Circle the ratios that you can use to form a proportion.
3
4
1
2
25
100
75
100
3. Cross out the proportion that does NOT have the same solution as the others.
n
12
17 5 20
17
12
n 5 20
n
20
17 5 12
20
17
n 5 12
bisector (noun)
BY
sek tur
Other Word Form: bisect (verb)
Definition: A bisector divides a whole into two equal parts.
Math Usage: A bisector is a point, segment, ray, or line that divides an angle or a
segment into two congruent angles or segments.
Use Your Vocabulary
Use the diagram at the right. Complete each statement with
the correct word from the list below. Use each word only once.
bisects
bisector
)
4. BD is the 9 of /ABC.
)
5. /ABC is 9 by BD .
D
bisected
bisector
bisected
)
bisects
Chapter 7
198
6. BD 9 /ABC.
A
B
C
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Vocabulary Builder
Theorem 7-4 Side-Splitter Theorem and Its Corollary
Side-Splitter Theorem
If a line is parallel to one side of a triangle and intersects the other two sides, then
it divides those sides proportionally.
YS
* ) * )
XR
.
If RS u u XY , then RQ 5
Q
S
R
SQ
7. If XR 5 4, RQ 5 4, and YS 5 5, then SQ 5
5 .
8. If XR 5 3, RQ 5 6, and YS 5 4, then SQ 5
8 .
Y
X
Corollary to the Side-Splitter Theorem
If three parallel lines intersect two transversals, then the segments intercepted
on the transversals are proportional.
A
a
X
B
b
WX
If a 6 b 6 c , then AB
BC 5 XY .
W
C
c
Y
Complete each proportion.
BC
XY
9. AB 5
WX
WY
AC
11. AB 5 WX
CB
YX
10. BA 5 XW
Problem 1 Using the Side-Splitter Theorem
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Got It? What is the value of a in the diagram at the right?
12. The value of a is found below. Use one of the reasons in the
box to justify each step.
Cross Products Property
Divide each side by 6.
Side-Splitter Theorem
Simplify.
a
a 4
12
18
Subtract 12a from each side.
a
12
a 1 4 5 18
18a 5 12a 1 48
18a 2 12a 5 12a 2 12a 1 48
Side-Splitter Theorem
Cross Products Property
Subtract 12a from each side.
6a 5 48
Simplify.
6a
48
6 5 6
Divide each side by 6.
a58
Simplify.
199
Lesson 7-5
Problem 2
Finding a Length
Got It? Camping Three campsites are shown in the diagram.
6.4
What is the length of Site C along the road?
8 yd
13. Let y be the length of Site C along the road. Use the
justifications at the right to find the value of y.
y
5
7.2
Corollary to Side-Splitter
Theorem
8
? y 5 46.08
8
?y
8
6.4
8
5
y5
46.08
yd
Site A
Site B
9 yd
7.2 yd
Site C
Cross Products Property
8
Divide each side by the
coefficient of y.
5.76
Simplify.
14. The length of Site C along the road is
5.76
yd.
Theorem 7-5 Triangle-Angle-Bisector Theorem
Triangle-Angle-Bisector Theorem
A
)
CD
CA
If AD bisects /CAB, then DB 5 BA .
C
B
D
Problem 3 Using the Triangle-Angle-Bisector Theorem
Got It? What is the value of y in the diagram at the right?
Write
Think
y
9.6
â
hsm11_gemc_0705_t93531
16
24
Theorem to write a proportion.
I can use the Triangle-Angle-Bisector
Then I can use the Cross-Products
Property.
Now I divide each side by 16
and simplify.
230.4
â16y
230.4
16
â
y â
16. The value of y is 14.4 .
Chapter 7
24
y
15. Complete the reasoning model below.
200
16
y
16
14.4
9.6
16
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
If a ray bisects an angle of a triangle, then it divides the opposite side into two
segments that are proportional to the other two sides of the triangle.
Lesson Check • Do you know HOW?
10
What is the value of x in the figure at the right?
30
17. Circle the proportion you can use to solve
the problem.
10
x
30 5 45
x
30
10 5 45
x
45
x
30
x 1 10 5 45
10
30
x 1 10 5 45
18. Solve the proportion.
10
x 1 10
5 30
45
10(45) 5 30(x 1 10)
45 5 3x 1 30
15 5 3x
55x
Lesson Check • Do you UNDERSTAND?
Error Analysis A classmate says you can use the Side-Splitter Theorem to find both
x and y in the diagram. Explain what is wrong with your classmate’s statement.
y
2
x
3
19. Cross out the lengths that are NOT parts of the sides intersected by the
parallel line.
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
2
2.4
3
7
2.4
7
x
y
20. Can you use the Side-Splitter Theorem to find x?
Yes / No
21. Can you use the Side-Splitter Theorem to find y?
Yes / No
22. Explain what is wrong with your classmate’s statement.
Explanations may vary. Sample: x is not part of the transversal so I cannot
_______________________________________________________________________
use the Side-Splitter Theorem to find x.
_______________________________________________________________________
Math Success
Check off the vocabulary words that you understand.
bisector
proportion
Side-Splitter Theorem
Rate how well you understand side and angle bisectors.
Need to
review
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2
4
6
8
Now I
get it!
10
201
Lesson 7-5