Identifying Similar Triangles 73 and Parallel Lines and Proportional Parts 74

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Identifying Similar Triangles (7-3) and Parallel
Lines and Proportional Parts (7-4)

• Note-taking is expected during this slide show!

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Lets look at the mathematics of the example
If the cross-products are equal, the traingles
are similar.
12x25300 and 15x20300
20x20400 and 25x16400
Since the cross-products of the ratios of the
corresponding sides are equal, the triangles are
similar.
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Determine whether each pair of triangles is
similar. Give a reason for your answer.
Two sets of corresponding angles are congruent
Similar by the AA similarity postulate.
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Two pairs of corresponding sides are
proportional, and their included angles are
congruent
Similar by the SAS similarity postulate
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Write a two-column proof to show that triangle
JLF is similar to triangle EDF, given that JL is
parallel to DE.
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Given JL is parallel to DE Prove JLF is
similar to EDF
Statement
Reason

• JL is parallel to DE
• Angle JLD Angle LDE
• Angle LJE Angle DEJ
• JLF is similar to EDF

• Given
• Alternate interior angles
• Alternate interior angles
• AA similarity postulate

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• EF Intersects AC and AB, and is parallel to CB
• The ratio of CE/EA is proportional to the ratio
  of BF/FA

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• Since the ratio of CE/EA is proportional to the
  ratio of BF/FA
• FE is parallel to CB

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• If E was the midpoint of AC, and F was the
  midpoint of AB
• EF would be parallel to CB and
• EF would be 1/2 the length of CB

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The ratio of 6/8 is proportional to the ratio of
15/x, so 6x 15 x 8 6x 120 x 120/6 X 20
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The ratio of (x6)/x is proportional to the ratio
of (30-9)/9, therefore 9(x6) x(30-9) 9x54
30x-9x 9x54 21x 54 12x x 54/12 x
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