Lesson 13.1 Similar Figures pp. 536-539
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Transcript of Lesson 13.1 Similar Figures pp. 536-539
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Lesson 13.1Similar Figures
pp. 536-539
Lesson 13.1Similar Figures
pp. 536-539
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Objectives:1. To define similar polygons.2. To apply proportions to problems
involving similar figures.
Objectives:1. To define similar polygons.2. To apply proportions to problems
involving similar figures.
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Similar polygonsSimilar polygons are polygons are polygons having corresponding angles that having corresponding angles that are congruent and corresponding are congruent and corresponding sides that are proportional. If sides that are proportional. If ABC and ABC and DEF are similar, the DEF are similar, the proper notation is proper notation is ABC ~ ABC ~ DEF. DEF.
DefinitionDefinitionDefinitionDefinition
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What exactly does ABC ~ DEF mean? What exactly does ABC ~ DEF mean?
A D, B E,& C F
A D, B E,& C F
FDFDCACA
EFEFBCBC
DEDEABAB
====
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A ratio is the comparison of two numbers. A proportion is an equation with two equal ratios. To solve a proportion, cross multiply.
A ratio is the comparison of two numbers. A proportion is an equation with two equal ratios. To solve a proportion, cross multiply.
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..151599
55xx
SolveSolve ==
33xx ==
4545xx1515 ==151599
55xx
==
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AA BB
CC
1616
88 1212A′A′ B′B′
C′C′
88
44 66
2211
161688
====ABAB
BBAA ′′′′
2211
8844
====ACAC
CCAA ′′′′
2211
121266
====BCBC
CCBB ′′′′
BCBCCCBB ′′′′
==ACAC
CCAA ′′′′==
ABABBBAA ′′′′
Therefore ABC ~ A′B′C′.Therefore ABC ~ A′B′C′.
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If the corresponding angles of two polygons are congruent and the corresponding sides are proportional, then you know the two figures are similar.
If the corresponding angles of two polygons are congruent and the corresponding sides are proportional, then you know the two figures are similar.
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Practice: Set up a proportion for the following dilation and solve for the missing term. 1. AB = 5, A′B′ = 75, CD = 3.
Find C′D′.
Practice: Set up a proportion for the following dilation and solve for the missing term. 1. AB = 5, A′B′ = 75, CD = 3.
Find C′D′.
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Practice: Set up a proportion for the following dilation and solve for the missing term. 2. A′B′ = 20, CD = 12, C′D′ = 8.
Find AB.
Practice: Set up a proportion for the following dilation and solve for the missing term. 2. A′B′ = 20, CD = 12, C′D′ = 8.
Find AB.
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Practice: If the figures are similar, find the unknown values.3.
Practice: If the figures are similar, find the unknown values.3.
33
66
44
xx
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Practice: If the figures are similar, find the unknown values.4.
Practice: If the figures are similar, find the unknown values.4.
101044
88
33
xxyy
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Practice: If the figures are similar, find the unknown values.5.
Practice: If the figures are similar, find the unknown values.5.
3333
5555
33
xx
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Homeworkpp. 538-539Homeworkpp. 538-539
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►A. ExercisesSolve each proportion.
3.
►A. ExercisesSolve each proportion.
3.63635454
xx66
==
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►A. ExercisesFind the ratio of the lengths in the right figure (image) to those in the left figure (preimage) for each pair of similar figures.
7.
►A. ExercisesFind the ratio of the lengths in the right figure (image) to those in the left figure (preimage) for each pair of similar figures.
7.
1212 33
88
441616
2211 44
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►A. ExercisesGiven that the figures are similar in each problem, find the length of the indicated sides.
11.
►A. ExercisesGiven that the figures are similar in each problem, find the length of the indicated sides.
11. 44
33 5555 33
44
xxyy
66
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►B. Exercises13. If LPQ ~ RST, what angles
are congruent, and what sides are proportional?
►B. Exercises13. If LPQ ~ RST, what angles
are congruent, and what sides are proportional?
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►B. Exercises15. Are congruent triangles also
similar?
►B. Exercises15. Are congruent triangles also
similar?
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■ Cumulative Review21. Find the center of the dilation. ■ Cumulative Review21. Find the center of the dilation.
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■ Cumulative Review22. Give the scale factor.■ Cumulative Review22. Give the scale factor.
AA
BB C’C’B’B’
A’A’
CC
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■ Cumulative Review23. If the image of a dilation is
congruent to the preimage, then what is the scale factor?
■ Cumulative Review23. If the image of a dilation is
congruent to the preimage, then what is the scale factor?
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■ Cumulative Review24. Classify three types of
dilations based on scale factors.
■ Cumulative Review24. Classify three types of
dilations based on scale factors.
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■ Cumulative Review25. Find A′B′C′, if P is the
center of a dilation with scale .
■ Cumulative Review25. Find A′B′C′, if P is the
center of a dilation with scale .
●P ●P
4433