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1 imilar Triangles UNIT BUN! reated by: THING GB

2 Unit 6 imilar Triangles: ample Unit Outline TOI HOWO Y 1 atios and roportions HW #1 Y 2 imilar Figures HW #2 Y 3 roving Triangles imilar:,, and HW #3 Y 4 Quiz 6-1 None Y 5 arallel ines & roportional arts HW #4 Y 6 arts of imilar Triangles HW #5 Y 7 Unit 6 eview tudy for Test Y 8 UNIT 6 TT None Gina Wilson (ll Things lgebra), 2014

3 Name: lass: Topic: ate: ain Ideas/Questions What is a TIO? ample: music store has 40 trumpets, 39 clarinets, 24 violins, 51 flutes, and 16 trombones in stock. Give each as a simplified ratio. Notes of quantities. Ways to represent a ratio: ; ; atios can be! 1. Trumpets to violins. 2. Flutes to clarinets. 3. Trombones to trumpets. 4. Violins to total instruments. tended atios of quantities. tended ratios are written as. 5. The ratio of two complementary angles is 3:7. Find the measures of both angles. Using atios to find ngles and ides: 6. The ratio of two supplementary angles is 4:1. Find the measures of both angles. 7. The ratio of the measures of the angles in a triangle is 4:7:9. Find the measures of the angles. 8. The ratio of the measures of the angles in a triangle is 11:2:5. Find the measure of the largest angle. Gina Wilson (ll Things lgebra), 2014

4 9. The ratio of the measures of the sides of a 10. triangle is 2:8:9. If the perimeter of the triangle is 76 inches, find the length of each side. The ratio of the measures of the sides of a triangle is 10:15:6. If the perimeter of the triangle is 217 meters, find the length of the shortest side. What is a OOTION? n that states two are equal. proportion is written as ross roduct roperty: For any proportion, amples: olve each proportion using the ross roduct roperty = = = = = = = = Gina Wilson (ll Things lgebra), 2014

5 Name: ate: Bell: Unit 6: imilar Triangles Homework 1: atio & roportion ** This is a 2-page document! ** irections: Write the ratio in simplest form elementary schools to 16 middle schools treadmills to 36 elliptical machines buses to 66 cars red marbles to 145 blue marbles 5. The hockey team played 82 regular season games last year. If they won 44 games, what is the ratio of wins to losses? 6. In the word FHIGHT what is the ratio of vowels to total letters? irections: Use the given ratios to solve each problem. 7. The ratio of the measures of two 8. The ratio of the measures of the three angles in complementary angles is 7:8. What is the a triangle is 2:9:4. Find the measures of the measure of the smaller angle? angles. 9. The ratio of the measures of the three angles in a triangle is 10:3:7. Find the measure of the largest angle. 10. The ratio of the measure of the verte angle to the base angle of an isosceles triangle is 8:5. Find the measure of the verte angle. 11. The ratio of the measures of the sides of a triangle is 21:8:14. If the perimeter of the triangle is 215 feet, find the length of each side. 12. The ratio of the measures of the sides of a triangle is 4:7:5. If the perimeter of the triangle is 128 yards, find the length of the longest side. Gina Wilson (ll Things lgebra), 2014

6 irections: olve each proportion = = = = = = = = Gina Wilson (ll Things lgebra), 2014

7 Name: lass: Topic: ate: ain Ideas/Questions imilar olygons Notes olygons with the same but different. olygons are similar if: (1) (2) The ratio of corresponding sides is called the. If polygons are similar, then their are also proportional. cale Factor {Order atters!} What is the scale factor of B to F? What is the scale factor of F to B? B What is the ratio of the perimeter of F to B? 27 F imilarity tatements ymbol for imilar: valid similarity statement must match corresponding angles and sides! Write a similarity statement for the triangles above: irections: ist all congruent angles and write a proportion that relates the corresponding sides. 1. J ~ N 2. XYZ ~ Y Y X J N Z ngles ides ngles ides Gina Wilson (ll Things lgebra), 2014

8 3. J ~ Q Q ngles ides J Using imilar Figures to olve for issing easures. 4. If the figures below are similar with a scale factor of 2:3, find the value of. 5. If the figures below are similar with a scale factor of 6:5, find the value of If B ~ F, find the value of. 7. If Q ~ WXYZ, find the value of. B F 28 Q 75 Z 32 Y 40 X W 8. If G ~ X, find the value of. G X If TY ~ H, find the value of. T Y H Gina Wilson (ll Things lgebra), 2014

9 ore ractice with <II FIGU> Given the similar polygons, use a proportion to find the value of each variable. 1. J ~ N 40 y N J 2. F ~ HJG G F y 15 H J 3. Q ~ TUV 54 U 24 Q V 36 T B ~ 20 8 B N ~ Q N Q Gina Wilson (ll Things lgebra), 2014

10 6. B ~ FG F B 42 G 7. N ~ Q N 7 9 Q 8. T ~ YZ 40 Y Z 5 T 9. ~ FG F G If ~ Q with a scale factor of 3:5, find the perimeter of Q. 15 Q 6 12 Gina Wilson (ll Things lgebra), 2014

11 Name: ate: Bell: Unit 6: imilar Triangles Homework 2: imilar Figures ** This is a 2-page document! ** irections: ist all congruent angles and write a proportion that relates the corresponding sides. 1. FGH ~ JH ngles ides G H F J irections: The pairs of polygons below are similar. Give the scale factor of figure to figure B B B If the scale factor of figure to figure B is 4:5, find the value of. 5. If the scale factor of figure to figure B is 7:2, find the perimeter of figure. 12 B 15 B If B ~, find the value of and y If J ~ N, find the value of. + 5 N J Gina Wilson (ll Things lgebra), 2014

12 8. If GH ~ F, find the value of G H F 9. If XYZ ~ T, find the value of. Y 5 3 T X 60 Z 10. If B ~, find the value of. B If J ~ N, find the value of N J 12. If B ~ GF, find the value of. F B G Gina Wilson (ll Things lgebra), 2014

13 Triangle imilarity ~ ngle-ngle imilarity ~ ide-ide ide-ide imilarity ~ ide-ngle ngle-ide imilarity If two corresponding angles are congruent, then the triangles are similar. If all corresponding sides are proportional, then the triangles are similar. If two corresponding sides are proportional and the included angles are congruent, then the triangles are similar. etermine if the eamples below are similar by ~. If yes, write a similarity statement. etermine if the eamples below are similar by ~. If yes, write a similarity statement. etermine if the eamples below are similar by ~. If yes, write a similarity statement. 1) B F 3) Q T U 5) 8 J 20 N 6 15 Y 2) W V X Z 4) G F H 6) B Gina Wilson (ll Things lgebra), 2014

14 OVING TING II { ~ etermine if the triangles are similar by ngle-ngle imilarity. 1) 2) F Q N G 3) 4) H 51 Y 39 W 68 B G 68 F 5) 6) Y 91 X Z 67 N 25 B Q { ~ etermine if the triangles are similar by ide-ide ide-ide imilarity. 7) 8) W 15 X 6 Y N V 8 U Gina Wilson (ll Things lgebra), 2014

15 9) 10) T 10 J T Z Y ) 12) Y 8 Z X 14.4 W V 12 B {~ etermine if the triangles are similar by ide-ngle ngle-ide imilarity. 13) F G 14) 24 J F Y 15) Q 16) F J G H 35 17) 18) W 15 Q G B 9 7 X Y Z Gina Wilson (ll Things lgebra), 2014

16 W II? irections: etermine whether the triangles are similar. If similar, state how (~, ~, or ~), and write a similarity statement. 1 2 V 35 3 F U N G W 16 T Q 6 X B Y F 30 T 20 J N Y H T U X 61 Z G 34 J Q Gina Wilson (ll Things lgebra), 2014

17 9 35 W T G B H I O V N U T N F B T H G Y T Z X 17 G H F 62 Q 31 H V Gina Wilson (ll Things lgebra), 2014

18 Name: ate: Bell: Unit 6: imilar Triangles Homework 3: roving Triangles imilar ** This is a 2-page document! ** irections: etermine whether the triangles are congruent by ~, ~, ~, or not similar T N G Q 44 J H F W Y 30 T 8 Z N 106 H F X Q 60 N N B J N T 72 U W H B V Gina Wilson (ll Things lgebra), 2014

19 G J 72 H Q 12 T 30 eview! 13. The ratios of the measures of the sides of a triangle is 4:10:7. Find the length of each side if the perimeter of the triangle is 252 meters. 14. The ratios of the measures of the angles of a triangle is 5:13:2. Find the measures of the angles. 15. If G ~ F, find the value of. F G 16. If TU ~, find the value of. T U Gina Wilson (ll Things lgebra), 2014

20 Name: lass: Topic: ate: ain Ideas/Questions Triangle roportionality THO Notes If a line is parallel to one side of a triangle and intersects the other two sides, then it divides the sides into segments of proportional lengths. B If, then. onverse of the Triangle roportionality Theorem: If, then. irections: Find the value of Gina Wilson (ll Things lgebra), 2014

21 irections: etermine if N is parallel to J J N N 5 J J N 37.5 roportional arts and IN If three or more parallel lines intersect two transversals, then they cut off the transversals proportionally. B F If, then. irections: Find the value of Gina Wilson (ll Things lgebra), 2014

22 Name: ate: Bell: Unit 6: imilar Triangles Homework 4: arallel ines & roportional arts ** This is a 2-page document! ** irections: olve for irections: etermine if T is parallel to Q 10 T Q 41.8 T 33 Q T 52 Gina Wilson (ll Things lgebra), 2014

23 irections: olve for Gina Wilson (ll Things lgebra), 2014

24 arts of imilar Triangles If two triangles are similar, then the following corresponding parts are also proportional to the corresponding sides: B F H G Q U T W V H G J I N ractice! Given the similar triangles, solve for. 1. TU ~ 2. GHI ~ T 16 W 19.2 U 24 I J 10 F G H 14 N 8 3. B ~ GF 4. Q ~ UT B H 24 G F Q T 42 U Gina Wilson (ll Things lgebra), 2014

25 5. Y ~ BH Y B X 2 H Triangle ngle Bisector Theorem n angle bisector in a triangle separates the opposite sides into two segments that are proportional to the lengths of the other two sides. B ractice! If represents an angle bisector, solve for J J J J J Gina Wilson (ll Things lgebra), 2014

26 Name: ate: Bell: Unit 6: imilar Triangles Homework 5: arts of imilar Triangles ** This is a 2-page document! ** irections: Given each pair of similar triangles, find the missing value. 1. B ~ HG; Find. 2. J ~ QN; Find. B F 14 G H J 30 N 42.9 O 39 Q 4. WVX ~ T; Find. V Y 27 X U T W 4. F ~ JHI; Find F. I G F H J 5. N ~ T; Find T. N U 26 T Q Gina Wilson (ll Things lgebra), 2014

27 irections: If Q represents an angle bisector, solve for Q 12.6 Q Q 9. Q Q Q Q Gina Wilson (ll Things lgebra), 2014

28 Unit 6 Test tudy Guide (imilar Triangles) Name: ate: Block: Topic 1: atio & roportion 1. The ratio of the measures of the angles in a triangle is 8:3:4. Find the measures of the angles. 2. The ratio of the measures of the sides of a triangle is 9:12:5. If the perimeter of the triangle is 130 feet, find the measures of the sides. Topic 2: imilar Figures 3. Find the scale factor of Figure to Figure B. 4. Find the scale factor of Figure B to Figure B B If J ~ VWU, find the value of. U J W V 6. If N ~ find the value of N Gina Wilson (ll Things lgebra), 2014

29 7. If F ~ J, find. J F 8. If Q ~ T, find T Q 9. If ~ WXY with a scale factor of 4:3, find the perimeter of WXY. X W Y Topic 3: roving Triangles imilar etermine if the triangles are similar, if possible, by ~, ~, or ~. If similar, complete the similarity statement B Q 47 imilar By: ~ imilar By: B ~ Gina Wilson (ll Things lgebra), 2014

30 Y F 8 N imilar By: YN ~ H imilar By: ~ 8 J T W 44 Q V 9 45 N imilar By: TH ~ imilar By: JN ~ Topic 4: arallel ines & roportional arts irections: olve for Gina Wilson (ll Things lgebra), 2014

31 irections: etermine if is parallel to B B Topic 5: arts of imilar Triangles irections: The triangles shown below are similar. olve for Gina Wilson (ll Things lgebra), 2014

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