6.6 use proportionality theorems
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Transcript of 6.6 use proportionality theorems
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6.66.6 Use Proportionality Theorems
Bell Thinger
ANSWER 8
1. Give the postulate or
theorem that justifies why
the triangles are similar.
2. Solve = .3216 12 – x
x
ANSWER AA Similarity Postulate
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6.6
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6.6Example 1
In the diagram, QS || UT , RS = 4,
ST = 6, and QU = 9. What is the
length of RQ ?
SOLUTION
Triangle Proportionality Theorem
Substitute.
Multiply each side by 9 and simplify.RQ = 6
RQQU
RSST
=
RQ9
46=
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6.6Example 2
Shoerack
SOLUTION
Find and simplify the ratios of lengths determined by
the shoerack.
CBBA
2733
=9
11=CD
DE4425
=
On the shoerack
shown, AB = 33 cm, BC = 27
cm, CD = 44 cm,and DE = 25 cm.
Explain why the gray shelf is
not parallel to the floor.
Because , BD is not parallel to AE .
So, the shelf is not parallel to the floor.
4425
911
=
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6.6Guided Practice
1. Find the length of YZ .
31511ANSWER
2. Determine whether PS || QR .
ANSWER parallel
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6.6
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6.6Example 3
In the
diagram, 1, 2, and 3 are all
congruent and GF = 120 yards, DE
= 150 yards, and CD = 300 yards.
Find the distance HF between
Main Street and South Main
Street.
City Travel
SOLUTION
Corresponding angles are congruent, so
FE, GD , and HC are parallel. Use Theorem 6.6.
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6.6
HG + GFGF
CD + DEDE
=
HGGF
CDDE
= Parallel lines divide transversals
proportionally.
Property of proportions
(Property 4)
Substitute.
HF = 360
HF120
300+150150=
450150
HF120
= Simplify.
Multiply each side by 120 and
simplify.
The distance between Main Street and South Main
Street is 360 yards.
Example 3
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6.6Example 4
SOLUTION
In the diagram, QPR RPS. Use
the given side lengths to find the
length of RS .
Because PR is an angle bisector of
QPS, you can apply Theorem 6.7. Let RS = x.
Then RQ = 15 – x.
7x = 195 – 13x Cross Products Property
x = 9.75 Solve for x.
RQRS
PQPS
=
15 – x
x=
73
Angle bisector divides opposite
side proportionally.
Substitute.
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6.6Guided Practice
Find the length of AB.
3. ANSWER 19.2
4. ANSWER 4 2
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6.6Exit Slip
Find the value of the variable.
1.ANSWER 12
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6.6
Find the value of the variable.
2.
ANSWER 13.5
Exit Slip
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6.6
Find the value of the variable.
ANSWER 23.8
3.
Exit Slip
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6.6
4. This diagram represents a tract of land being
developed for homes. Which lot has the greatest
perimeter?
ANSWER Lot B
Exit Slip
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6.6
No ANSWERANSWER Yes; XYZ ~ CBA
Exit Slip
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6.6
Homework
Pg 418-421
#5, 10, 16, 21, 24