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## Proportional Parts and Triangles

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**Vocabulary**Proportional Parts and Triangles What You'll Learn You will learn to identify and use the relationships between proportional parts of triangles. Nothing New!**intersects the other two sides of ΔPQR.**and P Q R Proportional Parts and Triangles In ΔPQR, Are ΔPQR and ΔPST, similar? corresponding angles PST PQR P P ΔPQR ~ ΔPST. Why? (What theorem / postulate?) S T AA Similarity**A**C B E D If Proportional Parts and Triangles parallel similar ΔABC ~ ΔADE.**Since**, ΔSVW ~ ΔSRT. Complete the proportion: R V S W T SV Proportional Parts and Triangles**A**C B D E Proportional Parts and Triangles proportional lengths**A**3 4 H G 5 x + 5 x B C Proportional Parts and Triangles**Brace**4 ft 6 ft 10 ft = 3 x =1 x ft 5 4 ft Proportional Parts and Triangles Jacob is a carpenter. Needing to reinforce this roof rafter, he must find the length of the brace. 4 x 4 10 10x = 16**A**6 4 C B 9 6 D E Triangles and Parallel Lines You know that if a line is parallel to one side of a triangle and intersects the other two sides, then it separates the sides into segments of proportional lengths (Theorem 9-5). The converse of this theorem is also true.**A**x D E 2x C B Triangles and Parallel Lines one-half**8**5 8 5 Triangles and Parallel Lines Use a theorem to find the length of segment DE. A x 11 D E 22 C B**M**1) MP || ____ A B AC N P C Triangles and Parallel Lines A, B, and C are midpoints of the sides of ΔMNP. Complete each statement. 28 2) If BC = 14, then MN = ____ s 3) If mMNP = s, then mBCP = ___ 4) If MP = 18x, then AC = __ 9x**E**8 A B 5 7 D F C Triangles and Parallel Lines A, B, and C are midpoints of the sides of ΔDEF. 1) Find DE, EF, and FD. 14; 10; 16 2) Find the perimeter of ΔABC 20 3) Find the perimeter of ΔDEF 40 4) Find the ratio of the perimeter of ΔABC to the perimeter of ΔDEF. 1:2 20:40 =**D**F G is the midpoint of BA E is the midpoint of AD H is the midpoint of CB C F is the midpoint of DC E H A G B Q1) What can you say about EF and GH ? (Hint:Draw diagonal AC .) Triangles and Parallel Lines ABCD is a quadrilateral. They are parallel Q2) What kind of figure is EFHG ? Parallelogram**D**A E B Measure AB, BC, DE, and EF. F C , , DE AB DE AB Calculate each set of ratios: DF BC EF AC Proportional Parts and Parallel Lines Hands-On On your given paper, draw two (transversals) lines intersecting the parallel lines. Label the intersections of the transversals and the parallel lines, as shown here. Do the parallel lines divide the transversals proportionally? Yes**A**D l m n B E C F BC DE DE AB EF AB BC AC EF DF DF AC , , = = = and Then Proportional Parts and Parallel Lines If l || m || n**=**= G U 12 15 a b c H V 18 x J W 1 x = 22 2 Proportional Parts and Parallel Lines Find the value of x. UV GH VW HJ 15 12 x 18 12x = 18(15) 12x = 270**A**D l m n B E C F AB BC, DE EF. Proportional Parts and Parallel Lines If l || m || n and Then**Since AB BC,**DE EF 5 = x Proportional Parts and Parallel Lines Find the value of x. 10 A B 10 Theorem 9 - 9 C (x + 3) = (2x – 2) x + 3 = 2x – 2 (2x – 2) 8 (x +3) 8 F E D**Proportional Parts and Parallel Lines**Homework: Wb: Pg 118-20 All