Download Dividing a decimal by a whole number

Similarity
Opening routine
Similarity
Opening routine
Identify the
corresponding parts of
ABC and DEF?
A  D
B  E
C  F
Side AB has to be
proportional to side DE
Side BC has to be
proportional to side EF
Side AC has to be
proportional to side DF
AB/DE = 18/9 = 2
BC/EF = 10/5 = 2
AC/DF = 14/6 = 2.33
AB/DE  AC/DF could be used to prove
that ABC and DEF are not similar.
The correct answer is D.
Topic IV:
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Objective: Use congruence and similarity
criteria for triangles to solve problems and to
prove relationships in geometric figures.
Essential Question: How do you use
proportions to find side lengths of similar
triangles?
Similar Triangles
Vocabulary
Proportion: Is the name that is given to
a statement that two ratios are equal.
In a proportion the cross products
are equal.
Similar triangles: Triangles are similar when they
preserve angle measures.
Similar triangles: Corresponding side lengths in
similar triangles are proportional.
Similar Triangles
Vocabulary
Scale factor: Is the ratio between corresponding
sides of similar triangles.
Angle–Angle Similarity (AA) Theorem: If two
angles of one triangle are congruent to two
angles of another triangle, then the two
triangles are similar.
Similar Triangles
Vocabulary
Side–Side–Side Similarity (SSS) Theorem: If the
corresponding side lengths of two triangles are
proportional, then the triangles are similar.
Side–Angle–Side Similarity (SAS) Theorem: If
two sides of one triangle have lengths that are
proportional to two sides of another triangle
and the included angles of those sides are
congruent, then the triangles are similar.
Similarity
MAFS.912.G-SRT.1.3: Use the properties of similarity
transformations to establish the AA criterion for two
triangles to be similar.
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MAFS.912.G-SRT.1.3: Use the properties of similarity
transformations to establish the AA criterion for two
triangles to be similar.
Similarity
MAFS.912.G-SRT.1.3: Use the properties of similarity
transformations to establish the AA criterion for two
triangles to be similar.
Similarity
MAFS.912.G-SRT.1.3: Use the properties of similarity
transformations to establish the AA criterion for two
triangles to be similar.
Similarity
MAFS.912.G-SRT.1.3: Use the properties of similarity
transformations to establish the AA criterion for two
triangles to be similar.
Similarity
MAFS.912.G-SRT.1.3: Use the properties of similarity
transformations to establish the AA criterion for two
triangles to be similar.
Similarity
MAFS.912.G-SRT.1.3: Use the properties of similarity
transformations to establish the AA criterion for two
triangles to be similar.
Similarity
Re-teach MAFS.912.G-SRT.1.3: Use the properties of
similarity transformations to establish the AA criterion for
two triangles to be similar.
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Similar triangles
Guided Practice – WE DO
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Similar triangles
Guided Practice – WE DO
As sides KL and GJ are parallel,
K  G because they are corresponding angles
H  H by Reflexive Property
HGJ  HKL by AA Theorem
KL/GJ = HK/HG
12/18 = x/15
18  x = 12  15
x = 12  15 / 18
x = 10
Corresponding sides are proportional
Substituting values
Applying Cross Products Property
Solving for x
The correct answer is C.
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Similar Triangles
Independent Practice - YOU DO
Triangle Similarity – Part 2
Exercises 1 – 2
Partitioning a Line Segment – Part 1
Exercises 1 - 4
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Triangles Similarity
Closure
Essential Question: How do you use
proportions to find side lengths of similar
triangles?
Similarity
Re-teach MAFS.912.G-SRT.1.3: Use the properties of
similarity transformations to establish the AA criterion for
two triangles to be similar.
Math Nation Section 7 Topic 1 Independent Practice
Math Nation Section 7 Topic 2 Independent Practice