Page 131 - Math Course 3 (Book 2)
P. 131
Proportional Parts of Triangles
Form the Triangle Proportionality Theorem, Proportional Segments
SV SU
VR = UT Example
Substitute the known measures.
3 = X MAPS
8 12 In the figure, Larch, Maple, and Nuthatch Streets
are all parallel. The figure shows the distances in
3(12) = 8x Cross products city blocks that the streets are apart. Find x.
36 = 8x Multiply.
36 = x Divide each side by 8. 26 13
8
1 16
4 = x Simplify.
2 Larch x
1 Nuthatch
Answer 4 Maple
2
Notice that the streets form a triangle that is cut by
Determine Parallel Lines parallel lines. So you can use the Triangle
Proportionality Theorem.
Example 26 X
13 = 16 Triangle Proportionality Theorem
1
In △DEF, DH = 18, HE = 36, and DG = GF. 26(16) = 13x Cross products
2
Determine whether GH || FE. Explain.
416 = 13x Multiply.
32 = x Divide each side by 13.
D
Answer 32
G H
F E
In order to show that GH || FE, we must show that
DG = DH DG = 1 GF, so DG = 1
GF HE 2 GF 2
DG 1 DH 18 1
Since = and = or
GF 2 HE 36 2
the sides have proportional length
since the segments have
DH
DG
Answer =
HE
GF proportional lengths,
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