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8-1.6 Prop & Similar Triangles

8-1.6 Prop & Similar Triangles - 8.6 Proportions...

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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=160-8x 22x=160 x=7.27 x 8 = 20 − x 14 Assignment Assignment ...
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