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8.6 Proportions & Similar Triangles
Unit IIA Day 9
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Do Now Solve each proportion. X= 4/3 Z = 49.5 Y= 1.4 Q = 2.5
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Discovery…
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Thm. 8.4 Triangle Proportionality Thm.
If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally. If TU || QS, then _________ RT/TQ = RU/US
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Thm. 8.5: Triangle Proportionality Converse
If a line divides two sides of a triangle proportionally, then it is parallel to the third side. If RT/TQ = RU/US, then __________ TU || QS
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Ex. 1: Finding the length of a segment
In the diagram AB || ED, BD = 8, DC = 4, and AE = 12. What is the length of EC? DC/BD = EC/AE – triangle proportionality thm. 4/8 = EC/12 – substitute 48 = 8EC – Cross multiply EC = 6
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Ex. 1A In the diagram UY is parallel to VX, UV=3 , UW=18, and XW=16. What is the length of YX? 3.2
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Ex. 2: Determining Parallels
Given the diagram, determine whether MN || GH. LM/MG = 56/21 = 8/3 LN/NH = 48/16 = 3/1 8/3 ≠ 3/1 MN is not parallel to GH.
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Ex. 2A Given the diagram, determine whether PQ is parallel to TR.
Yes (3/8)
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Thm. 8.6 If three parallel lines intersect two transversals, then they divide the transversals proportionally. If r || s || t and l and m intersect them, then ___________ UW/ WY = VX/ XZ
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Ex. 3: Using Proportionality Theorems
In the diagram 1 2 3, and PQ = 9, QR = 15, and ST = 11. What is the length of TU? Because corresponding angles are congruent, the lines are parallel and you can use Theorem 8.6 PQ/QR = ST/TU -- Parallel lines divide transversals proportionally. 9/15 = 11/TU – Substitute 9TU = 15*11 – Cross multiply TU = (15*11)/9 = 55/3 = 18 1/3
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Ex. 3A In the diagram, 1 2 3, AB = 6, BC = 9, EF = 8. What is x? 16/3
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Closure Explain what you know about a triangle cut by a segment that’s parallel to one of its sides.
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