7.1 Ratios and Proportions Notes

Transcription

1 7.1 Ratios and Proportions Notes Ratio Proportion olve the proportions: 1. 5 = x x 5 1 = x + 1 5x 4 = 5 4. x 11 4 = = 2x + 5. = 7 x x + 1

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3 7.1 Ratios and Proportions Notes Write and solve a proportion to answer each question 1. If ou bu 1 pound of beef containing grams of fat, then how much fat will be in 15.5 pounds? 2. The scale on a map sas 1.5cm is 0 miles. If two cities are 2.2cm apart, how man miles apart are the?. n airplane has a length of 78 meters and a wingspan of 0 meters. If a model of the plane has a wingspan of cm, how long is the model? 4. If a paint compan can paint 00 square feet in 2 hours, how long will it take them to paint 20 square feet? 5. In a school the ratio of teachers to students is 1 to 2. If there are 48 teachers, how man students are there?

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5 7.2 imilar Figures Notes imilar Figures cale Factor Determine if the figures are similar. Explain wh or wh not. Write a similarit statement if the figures are similar D K H B 4 J 2 I 2 2. Y Q 7 R Z 0 0 X. O N E 5 F H G L 7 M

6 7.2 imilar Figures Notes The figures are similar, find x and. Write the cale Factor x x The figures are similar, Find B.. x - B Q 7 R T D

7 opright Glencoe/McGraw-Hill, a division of The McGraw-Hill ompanies, Inc. NME DTE PERIOD 7-2 kills Practice imilar Polgons Determine whether each pair of figures is similar. Justif our answer. 1. B 2. E D 7 F P Q R Z 7.5 W Y X 7.5 Each pair of polgons is similar. Write a similarit statement, and find x, the measure(s) of the indicated side(s), and the scale factor.. G H 4. T and U 14 D 1 B 2 E 7 H F 1 x G W 4 4 Y X x 5 x 5 T U 5. W T. T and P P 5 Q R T U x 1 V W M 8 L N P x 2 T x 1 hapter 7 1 Glencoe Geometr

8 How an You Prove Triangles IMILR?

9 NME DTE PERIOD 7- tud Guide and Intervention imilar Triangles Identif imilar Triangles Here are three was to show that two triangles are similar. imilarit imilarit imilarit Two angles of one triangle are congruent to two angles of another triangle. The measures of the corresponding sides of two triangles are proportional. The measures of two sides of one triangle are proportional to the measures of two corresponding sides of another triangle, and the included angles are congruent. Example 1 Determine whether the Example 2 Determine whether the triangles are similar. triangles are similar. 8 D B D F 2 B 8 2 EF 1 2 B D E 15 B DEF b imilarit. F 15 E M 70 N Q 4 P 70 R 8 4 8, so M N N P. QR R m N m R, so N R. NMP RQ b imilarit. Exercises opright Glencoe/McGraw-Hill, a division of The McGraw-Hill ompanies, Inc. Determine whether each pair of triangles is similar. Justif our answer Lesson 7- hapter 7 21 Glencoe Geometr

10 opright Glencoe/McGraw-Hill, a division of The McGraw-Hill ompanies, Inc. NME DTE PERIOD 7- tud Guide and Intervention (continued) imilar Triangles Use imilar Triangles imilar triangles can be used to find measurements. Example 1 B DEF. Example 2 person feet tall casts Find x and. a 1.5-foot-long shadow at the same time B that a flagpole casts a 7-foot-long E shadow. How tall is the flagpole? B D F EF 18 x D x F B B D E EF x (18 ) 24 x 1.5 ft ft 7 ft? The sun s ras form similar triangles. Using x for the height of the pole, x 1.5, 7 so 1.5x 42 and x 28. The flagpole is 28 feet tall. Exercises Each pair of triangles is similar. Find x and x x x x x x The heights of two vertical posts are 2 meters and 0.45 meter. When the shorter post casts a shadow that is 0.85 meter long, what is the length of the longer post s shadow to the nearest hundredth? hapter 7 22 Glencoe Geometr

11 NME DTE PERIOD 7- kills Practice imilar Triangles Determine whether each pair of triangles is similar. Justif our answer. 1. Y 2. T 21 1 R W X B R Q P. P 4. T U J M 21 0 K M Q 0 T R LGEBR Identif the similar triangles, and find x and the measures of the indicated sides. 5. and E D. J L and L M opright Glencoe/McGraw-Hill, a division of The McGraw-Hill ompanies, Inc. J x 1 x 18 E 15 B 1 x 5 D K 7. E H and E F 8. V T and T H F x 4 E 14 V x x 5 G R T D U L x N 4 M Lesson 7- hapter 7 2 Glencoe Geometr

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