Parallel Lines and Proportional Parts

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Parallel Lines and Proportional Parts

• Chapter 7-4

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Lesson 4 MI/Vocab

• Use proportional parts of triangles.

• Divide a segment into parts.

• midsegment

Standard 12.0 Students find and use measures of
sides and of interior and exterior angles of
triangles and polygons to classify figures and
solve problems. (Key)
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Triangle Proportionality Theorem

• If a line parallel to one side of a triangle
  intersects the other two sides, then it divides
  the two sides proportionally.
• The converse is true also.

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Example 1
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Lesson 4 Ex1
Find the Length of a Side
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Lesson 4 Ex1
Find the Length of a Side
Substitute the known measures.
Cross products
Multiply.
Divide each side by 8.
Simplify.
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Lesson 4 CYP1
A. 2.29 B. 4.125 C. 12 D. 15.75
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Lesson 4 Ex2
Determine Parallel Lines
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Lesson 4 Ex2
Determine Parallel Lines
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Lesson 4 CYP2

1. A
2. B
3. C

A. yes B. no C. cannot be determined
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Midsegment Theorem

• The midsegment connecting the midpoints of two
  sides of the triangle is parallel to the third
  side and is half as long.

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Lesson 4 Ex3
Midsegment of a Triangle
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Lesson 4 Ex3
Midsegment of a Triangle
Answer D (0, 3), E (1, 1)
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Lesson 4 Ex3
Midsegment of a Triangle
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Lesson 4 Ex3
Midsegment of a Triangle
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Lesson 4 Ex3
Midsegment of a Triangle
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Lesson 4 Ex3
Midsegment of a Triangle
First, use the Distance Formula to find BC and DE.
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Lesson 4 Ex3
Midsegment of a Triangle
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Lesson 4 CYP3
A. W (0, 1), Z (1, 3) B. W (0, 2), Z (2,
3) C. W (0, 3), Z (2, 3) D. W (0, 2), Z (1, 3)
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Lesson 4 CYP3

1. A
2. B

A. yes B. no
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Lesson 4 CYP3

1. A
2. B

A. yes B. no
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Parallel Proportionality Theorem

• If 3 // lines intersect two transversals, then
  they divide the transversals proportionally.

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Example 2
Find ST
Parallel Proportionality Theorem
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Example 4
Solve for x and y
Solving for x
What is JL?
37.5 x
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Example 4
Solve for x and y
Solving for y
?JKL?JMN AA?Theorem
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Lesson 4 Ex4
Proportional Segments
MAPS In the figure, Larch, Maple, and Nuthatch
Streets are all parallel. The figure shows the
distances in city blocks that the streets are
apart. Find x.
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Lesson 4 Ex4
Proportional Segments
Notice that the streets form a triangle that is
cut by parallel lines. So you can use the
Triangle Proportionality Theorem.
Triangle Proportionality Theorem
Cross products
Multiply.
Divide each side by 13.
Answer 32
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Lesson 4 CYP4
In the figure, Davis, Broad, and Main Streets are
all parallel. The figure shows the distances in
city blocks that the streets are apart. Find x.
A. 4 B. 5 C. 6 D. 7
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Lesson 4 Ex5
Congruent Segments
Find x and y.
To find x
Given
Subtract 2x from each side.
Add 4 to each side.
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Lesson 4 Ex5
Congruent Segments
To find y
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Lesson 4 Ex5
Congruent Segments
Equal lengths
Multiply each side by 3 to eliminate the
denominator.
Subtract 8y from each side.
Divide each side by 7.
Answer x 6 y 3
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Lesson 4 CYP5
Find a.
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Lesson 4 CYP5
Find b.
A. 0.5 B. 1.5 C. 6 D. 1
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Homework

• Chapter 7-4
• Pg 410
• 13-21, 26 27, 32 36, 61