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7-4 Parallel Line and Proportional Parts.

7-4 Parallel Line and Proportional Parts. You used proportions to solve problems between similar triangles. Use proportional parts within triangles. Use proportional parts with parallel lines.

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7-4 Parallel Line and Proportional Parts.

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  1. 7-4 Parallel Line and Proportional Parts. You used proportions to solve problems between similar triangles. • Use proportional parts within triangles. • Use proportional parts with parallel lines.

  2. When a triangle contains a line that is parallel to one of its sides, the two triangles formed can be proved similar using AA Similarity Postulate. Since the triangles are similar, their sides are proportional. p. 490

  3. Substitute the known measures. Cross Products Property Multiply. Divide each side by 8. Simplify.

  4. A. 2.29 B. 4.125 C. 12 D. 15.75

  5. p. 491

  6. Since the sides are proportional. In order to show that we must show that Answer: Since the segments have proportional lengths, GH || FE.

  7. A. yes B. no C. cannot be determined

  8. Midsegment of a Triangle A midsegment of a triangle – a segment with endpoints that are the midpoints of two sides of the triangle. Every triangle has 3 midsegments. p. 491

  9. Definition A segment whose endpoints are the midpoints of two of its sides is a midsegment of a triangle. midsegment

  10. X M N Y Z Midsegment Theorem for Triangles A segment whose endpoints are the midpoints are the midpoints of two sides of a triangle is parallel to the third side and half its length. MN = ½ YZ

  11. ED = AB Triangle Midsegment Theorem A. In the figure, DE and EF are midsegments of ΔABC. Find AB. 5 = AB Substitution 1 1 __ __ 2 2 10 = AB Multiply each side by 2. Answer:AB = 10

  12. FE = BC Triangle Midsegment Theorem B. In the figure, DE and EF are midsegments of ΔABC. Find FE. FE = (18) Substitution 1 __ 1 __ 2 2 FE = 9 Simplify. Answer:FE = 9

  13. C. In the figure, DE and EF are midsegments of ΔABC. Find mAFE. By the Triangle Midsegment Theorem, AB || ED. AFEFED Alternate Interior Angles Theorem mAFE = mFED Definition of congruence mAFE = 87 Substitution Answer:mAFE= 87

  14. A. In the figure, DE and DF are midsegments of ΔABC. Find BC. A. 8 B. 15 C. 16 D. 30

  15. B. In the figure, DE and DF are midsegments of ΔABC. Find DE. A. 7.5 B. 8 C. 15 D. 16

  16. C. In the figure, DE and DF are midsegments of ΔABC. Find mAFD. A. 48 B. 58 C. 110 D. 122

  17. MAPS In the figure, Larch, Maple, and Nuthatch Streets are all parallel. The figure shows the distances in between city blocks. Find x. Notice that the streets form a triangle that is cut by parallel lines. So you can use the Triangle Proportionality Theorem. Triangle Proportionality Theorem Cross Products Property Multiply. Divide each side by 13. Answer:x = 32

  18. In the figure, Davis, Broad, and Main Streets are all parallel. The figure shows the distances in between city blocks. Find x. A. 4 B. 5 C. 6 D. 7

  19. p. 493

  20. ALGEBRA Find x and y. To find x: 3x – 7 = x + 5 Given 2x – 7 = 5 Subtract x from each side. 2x = 12 Add 7 to each side. x = 6 Divide each side by 2. To find y: The segments with lengths 9y – 2 and 6y + 4 are congruent since parallel lines that cut off congruent segments on one transversal cut off congruent segments on every transversal. 9y – 2 = 6y + 4 Definition of congruence 3y – 2 = 4 Subtract 6y from each side. 3y = 6 Add 2 to each side. y = 2 Divide each side by 3.

  21. x 6.2 2x 5x−57 17 x Solve for x 12.4 x = 8.5 2x = ½ (5x−57) 4x = 5x −57 −x = −57 x = 57

  22. 7-4 Assignment Page 495, 10-24 even,

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