# 7-4 Parallel Line and Proportional Parts.

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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. You used proportions to solve problems between similar triangles.
• Use proportional parts within triangles.
• Use proportional parts with parallel lines.
• 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 Substitute the known measures. its sides, the two triangles formed can be proved similar using AA Similarity Postulate. Since the triangles are similar, their sides are proportional. Cross Products Property Multiply. Divide each side by 8. Simplify. A. its sides, the two triangles formed can be proved similar using AA Similarity Postulate. Since the triangles are similar, their sides are proportional. 2.29 B. 4.125 C. 12 D. 15.75 p. 491 its sides, the two triangles formed can be proved similar using AA Similarity Postulate. Since the triangles are similar, their sides are proportional. Since the sides are proportional. In order to show that we must show that Answer: Since the segments have proportional lengths, GH || FE. A. sides are proportional. yes B. no C. cannot be determined Midsegment of a Triangle sides are proportional. 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 Definition sides are proportional. A segment whose endpoints are the midpoints of two of its sides is a midsegment of a triangle. midsegment X sides are proportional. 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 ED sides are proportional. = 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 FE sides are proportional. = 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 C. sides are proportional. 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 A. sides are proportional. In the figure, DE and DF are midsegments of ΔABC. Find BC. A. 8 B. 15 C. 16 D. 30 B. sides are proportional. In the figure, DE and DF are midsegments of ΔABC. Find DE. A. 7.5 B. 8 C. 15 D. 16 C. sides are proportional. In the figure, DE and DF are midsegments of ΔABC. Find mAFD. A. 48 B. 58 C. 110 D. 122 MAPS sides are proportional.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 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 p. 493 parallel. The figure shows the distances in between city blocks. Find ALGEBRA parallel. The figure shows the distances in between city blocks. Find 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. x parallel. The figure shows the distances in between city blocks. Find 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 7-4 Assignment parallel. The figure shows the distances in between city blocks. Find Page 495, 10-24 even,
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