Warm Up

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Warm Up
Problem of the Day
Lesson Presentation
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Warm Up Find the cross products, then tell
whether the ratios are equal.
16 6
40 15
,
1.
240 240 equal
3 8
18 46
,
2.
8 9
24 27
,
3.
216 216 equal
28 12
42 18
,
4.
504 504 equal
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Problem of the Day Every 8th telephone pole along
a road has a red band painted on it. Every 14th
pole has an emergency call phone on it. What is
the number of the first pole with both a red band
and a call phone?
56
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Learn to use ratios to determine if two figures
are similar.
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Insert Lesson Title Here
Vocabulary
similar corresponding sides corresponding angles
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Octahedral fluorite is a crystal found in nature.
It grows in the shape of an octahedron, which is
a solid figure with eight triangular faces. The
triangles in different-sized fluorite crystals
are similar figures. Similar figures have the
same shape but not necessarily the same size.
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Matching sides of two or more polygons are called
corresponding sides, and matching angles are
called corresponding angles.
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SIMILAR FIGURES
Two figures are similar if The measures of their corresponding angles are equal. The ratios of the lengths of the corresponding sides are proportional.
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Additional Example 1 Determining Whether Two
Triangles Are Similar
Identify the corresponding sides in the pair of
triangles. Then use ratios to determine whether
the triangles are similar.
E
16 in
10 in
A
C
28 in
D
4 in
7 in
40 in
F
B
AB DE
BC EF
AC DF
Write ratios using the corresponding sides.
4 16
7 28
10 40
Substitute the length of the sides.
1 4
1 4
1 4
Simplify each ratio.
Since the ratios of the corresponding sides are
equivalent, the triangles are similar.
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Check It Out Example 1
Identify the corresponding sides in the pair of
triangles. Then use ratios to determine whether
the triangles are similar.
E
9 in
9 in
A
C
21 in
D
3 in
7 in
27 in
F
B
AB DE
BC EF
AC DF
Write ratios using the corresponding sides.
3 9
7 21
9 27
Substitute the length of the sides.
1 3
1 3
1 3
Simplify each ratio.
Since the ratios of the corresponding sides are
equivalent, the triangles are similar.
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Additional Example 2 Determining Whether Two
Four-Sided Figures are Similar
Tell whether the figures are similar.
The corresponding angles of the figures have
equal measure.
Write each set of corresponding sides as a ratio.
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Additional Example 2 Continued
MN QR
NO RS
OP ST
MP QT
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Additional Example 2 Continued
Determine whether the ratios of the lengths of
the corresponding sides are proportional.
Write ratios using corresponding sides.
Substitute the length of the sides.
Simplify each ratio.
Since the ratios of the corresponding sides are
equivalent, the figures are similar.
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Check It Out Example 2
Tell whether the figures are similar.
The corresponding angles of the figures have
equal measure.
Write each set of corresponding sides as a ratio.
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Check It Out Example 2 Continued
MN QR
NO RS
OP ST
MP QT
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Check It Out Example 2 Continued
Determine whether the ratios of the lengths of
the corresponding sides are proportional.
Write ratios using corresponding sides.
Substitute the length of the sides.
Simplify each ratio.
Since the ratios of the corresponding sides are
equivalent, the figures are similar.
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Insert Lesson Title Here
Lesson Quiz Part I
Tell whether the figures are similar. 1.
similar
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Insert Lesson Title Here
Lesson Quiz Part II
Tell whether the figures are similar. 2.
not similar