Parts of Similar Triangles

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Chapter 7-5

• Parts of Similar Triangles

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Lesson 5 Menu
Five-Minute Check (over Lesson 7-4) Main
Ideas California Standards Theorem 7.7
Proportional Perimeters Theorem Example 1
Perimeters of Similar Triangles Theorems Special
Segments of Similar Triangles Example 2 Write a
Proof Example 3 Medians of Similar
Triangles Example 4 Solve Problems with Similar
Triangles Theorem 7.11 Angle Bisector Theorem
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Lesson 5 MI/Vocab
Standard 4.0 Students prove basic theorems
involving congruence and similarity. (Key)

• Recognize and use proportional relationships of
  corresponding perimeters of similar triangles.

• Recognize and use proportional relationships of
  corresponding angle bisectors, altitudes, and
  medians of similar triangles.

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Proportionate Perimeters of Polygons (try saying
that 10 times fastquietly!!!)

• If two polygons are similar, then the ratio of
  their perimeters is equal to the ratios of their
  corresponding side lengths.

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Lesson 5 Ex1
Perimeters of Similar Triangles
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Lesson 5 Ex1
Perimeters of Similar Triangles
Proportional Perimeter Theorem
Substitution.
Cross products
Multiply.
Divide each side by 16.
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Lesson 5 CYP1
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Similar Triangle Proportionality

• If two triangles are similar, then the ratio of
  any two corresponding lengths (sides, perimeters,
  altitudes, medians and angle bisector segments)
  is equal to the scale factor of the similar
  triangles.

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Example

• Find the altitude QS.

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Lesson 5 CYP2
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Lesson 5 Ex3
Medians of Similar Triangles
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Lesson 5 Ex3
Medians of Similar Triangles
Write a proportion.
EG 18, JL x, EF 36, and JK 56
Cross products
Divide each side by 36.
Answer Thus, JL 28.
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Lesson 5 CYP3
A. 2.8 B. 17.5 C. 3.9 D. 0.96

1. A
2. B
3. C
4. D

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Lesson 5 Ex4
Solve Problems with Similar Triangles
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Lesson 5 Ex4
Solve Problems with Similar Triangles
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Lesson 5 Ex4
Solve Problems with Similar Triangles
Write a proportion.
Cross products
Simplify.
Divide each side by 80.
Answer The height of the pole is 15 feet.
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Lesson 5 CYP4
A. 10.5 in B. 61.7 in C. 21 in D. 28 in
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Triangle Bisector Theorem

• If a ray bisects an angle of a triangle, then it
  divides the opposite side into segments whose
  lengths are proportional to the lengths of the
  other two sides.

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Example 3
Find DC
14-x
Triangle Bisector Thm.
x
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Homework

• Chapter 7-5
• Pg 419
• 1-13 skip 3, 19-22,
• 25-26, 39-40