Unformatted text preview: 8.6 Proportions and ~ ∆ s
Pg 498 Thm 8.4 Thm ∆ proportionality thm
• If a line  to one side of a ∆ intersects If  the other two sides, then it divides the 2 sides proportionally. sides A If seg BE  seg CD, then If  B > E AB AE = BC ED
D C > Thm 8.5 Thm converse of ∆ proportionality thm converse
• If a line divides 2 sides of a triangle If proportionally then it is ll to the 3rd proportionally side. side. P Q R If PQ = TS , QR SR then seg PT then  seg QS.  T S Example Example is seg PQ ll seg QS?
Q P 9 T S 26 R 9.75 9 9.75 = 24 26
234=234 YES! 24 Thm 8.6 Thm
• If 3 ll lines intersect 2 transversals, If then they divide the transversals proportionally. proportionally. A B C s > > > D E F t n l AB DE = BC EF
m Thm 8.7 Thm
• If a ray bisects an ∠ of a ∆ , then it If then divides the opposite side into segs whose lengths are proportional to the lengths of the other sides. lengths B
( If ray BD bisects ∠ ABC, then If ) AD AB = DC CB
C A D Example in the diagram, ∠ 1≅ ∠ 2≅ ∠ 3
A 1 6 B 2 9 C 3 6 x = 9 8
D 9x=48 x≈5.33 X E 8 F Example: find x
)
) 14 8 x 20 14x=1608x 22x=160 x=7.27 x 8 = 20 − x 14 Assignment Assignment ...
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 Spring '11
 Jackson
 Trigraph, thm, seg QS., proportionality thm, proportionality thm converse

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