7-4 Parallel Line and Proportional Parts.

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7-4 Parallel Line and Proportional Parts.
You used proportions to solve problems between
similar triangles.

• Use proportional parts within triangles.

• Use proportional parts with parallel lines.

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When a triangle contains a line that is parallel
to one of its sides, the two triangles formed can
be proved similar using AA Similarity Postulate.
Since the triangles are similar, their sides are
proportional.
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Substitute the known measures.
Cross Products Property
Multiply.
Divide each side by 8.
Simplify.
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A. 2.29 B. 4.125 C. 12 D. 15.75
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A. yes B. no C. cannot be determined
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Midsegment of a Triangle
A midsegment of a triangle a segment with
endpoints that are the midpoints of two sides of
the triangle. Every triangle has 3 midsegments.
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Definition
A segment whose endpoints are the midpoints of
two of its sides is a midsegment of a triangle.
midsegment
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Midsegment Theorem for Triangles
A segment whose endpoints are the midpoints are
the midpoints of two sides of a triangle is
parallel to the third side and half its length.
MN ½ YZ
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10 AB Multiply each side by 2.
Answer AB 10
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FE 9 Simplify.
Answer FE 9
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?AFE ? ?FED Alternate Interior Angles
Theorem m?AFE m?FED Definition of
congruence m?AFE 87 Substitution
Answer m?AFE 87
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A. 8 B. 15 C. 16 D. 30
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A. 7.5 B. 8 C. 15 D. 16
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A. 48 B. 58 C. 110 D. 122
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MAPS In the figure, Larch, Maple, and Nuthatch
Streets are all parallel. The figure shows the
distances in between city blocks. Find x.
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 Property
Multiply.
Divide each side by 13.
Answer x 32
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In the figure, Davis, Broad, and Main Streets are
all parallel. The figure shows the distances in
between city blocks. Find x.
A. 4 B. 5 C. 6 D. 7
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ALGEBRA Find x and y.
To find x
3x 7 x 5 Given 2x 7 5 Subtract x from
each side. 2x 12 Add 7 to each side. x
6 Divide each side by 2.
To find y
The segments with lengths 9y 2 and 6y 4
are congruent since parallel
lines that cut off congruent segments on one
transversal cut off congruent segments on every
transversal.
9y 2 6y 4 Definition of congruence 3y 2
4 Subtract 6y from each side. 3y 6 Add 2 to
each side. y 2 Divide each side by 3.
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Solve for x
12.4
x 8.5
2x ½ (5x-57) 4x 5x -57 -x -57 x 57
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7-4 Assignment
Page 495, 10-24 even,