7'5 Proportions and Similar Triangles 22708

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7.5 Proportions and Similar Triangles 2/27/08

• 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.
• In , if ,
  then .

R
T
U
Q
S
2
Find Segment Lengths

• Find the value of x.

C
x
4
D
E
12
8
A
B
3
Find Segment Lengths

• Find the value of y.

R
9
Q
3
P
S
y
T
20
4
Converse of the Triangle Proportionality Theorem

• If a line divides two sides of a triangle
  proportionally, then it is parallel to the third
  side.
• In if then

R
T
U
S
Q
5
Determine Parallels

• Given the diagram, determine whether MN is
  parallel to GH.
• Find and simplify the ratios of the two sides
  divided by MN.
• Answer Because , MN is not
  parallel to GH.

G
21
M
56
H
16
L
N
48
6
The Midsegment Theorem

• Midsegment of a triangle a segment that
  connects the midpoints of two sides of a
  triangle.
• Midsegment Theorem
• The segment connecting the midpoints of two sides
  of a triangle is parallel to the third side and
  is half as long.
• In , if and
  then
• and

C
D
E
B
A
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Use the Midsegment Theorem

• Find the length of DE.
• DE 1 AB 1 (10) 5
• 2 2
• Length of DE is 5.

C
D
E
B
A
10
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More Practice!!!

• Textbook p. 390 391 10 28 even.
• Homework worksheet 7.5