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Geometry Name: __________________________ Unit 6 – Similarity Date: ___________________________ Ratio - ________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ Examples: ______________ ________________ Ratios can be written in three different ways: 1.) 2.) 3.) These are all equivalent ratios and they represent the ratio of ______________________ ______________________________________________________________________ Ratios are usually expressed in simplest form. This means that for a final answer you should reduce all ratios. You reduce ratios just like you would reduce a fraction. Ex1: Ex2: Ex3: When simplifying ratios, the units of each number must be the same. Ex1: Ex2: Geometry Name: __________________________ Unit 6 – Similarity Date: ___________________________ How can we apply ratios to word problems? Example 1: The ratio of two supplementary angles is _____________. Find the measure of each angle. Steps for completing ratio word problems: 1. __________________________________________________________ 2. __________________________________________________________ 3. __________________________________________________________ 4. __________________________________________________________ Example 2: The measure of the angles in a triangle are in the ratio ________________. Find the measure of each angle. Example 3: ___________ prize money is to be allotted to the first, second, and third place winners of a competition in the ratio __________________. Determine how much money each winner should receive. Geometry Name: __________________________ Unit 6 – Similarity Date: ___________________________ Proportion - ____________________________________________________________ ______________________________________________________________________ Ex1: Ex2: We can use algebra to solve for unknowns within proportions. To solve a proportion you must: 1. __________________________________________________________ 2. __________________________________________________________ 3. __________________________________________________________ 4. __________________________________________________________ Ex1. Ex2. Ex3. Ex4. Ex5. Geometry Name: __________________________ Unit 6 – Similarity Date: ___________________________ Where else do we see ratios and proportions? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ Example: ______________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ Ex 1. On a map every _______ equals ________. You measure the distance between your house and your friend’s house as _________ on the map. How many miles apart do you really live? Ex 2. On a scale drawing every _________ represents ________. If you measure an object on the drawing as ________, how long is it really? Ex 3. On a blueprint _______ equals ________. If a room is really ________ long, how long would it appear on the blueprint? Ex 4. If ______ bags of apples cost ________, then how much does ________ bags of apples cost? Geometry Name: ___________________________________ Unit 6 WS 5 (Ratios) Date: ____________________________________ Directions: Simplify each ratio. 1. 15 35 2. 21 14 3. 55 11 4. 52 8 5. 5a 10a 6. 2a 2 34a 3 7. 22a 4b 55ab 2 8. 37a 7b 51a 5 9. 42cm 1m 10. 18mm 3cm 11. 13. 15in 3ft 14. 4ft 16in 15. 2km 350m 1760ft 1mi 12. 5m 324cm 16. 15ft 3yd Geometry Name: ___________________________________ Unit 6 WS 5 (Ratio Apps) Date: ____________________________________ Directions: Solve each word problem. Show all work; label all answers. 1. The ratio of two complementary angles is 2:3. Find the measure of each angle. 2. The ratio of the six angles in a hexagon (1, 2, 3, 4, 5, and 6) is 2:2:3:3:4:4. Find the measure of each angle. m1 = _______ m2 = _______ m3 = _______ m4 = _______ m1 = _______ m5 = _______ m2 = _______ m6 = _______ 3. The interior angle measures of a quadrilateral (1, 2, 3, and 4) are in the ratio 3:4:5:6. Find the measure of each angle. 4. The ratio of two supplementary angles is 4:5. Find the measure of each angle. m1 = _______ m2 = _______ m3 = _______ m1 = _______ m4 = _______ m2 = _______ 5. Prize money for a contest must be allotted in the following ratio to the top five winners: 6:4:3:2:1. The total amount of prize money is $5,000. Determine how much money each person receives. 6. Three students get in trouble at school. They must serve a total of 18 hours of detention. The detentions will be allotted in the ratio 2:3:4 for Adam, Alan, and Aaron respectively. Determine how much time each student will serve. First: __________ Second: ________ Third: _________ Adam: _______ Fourth: ________ Alan: ________ Fifth: __________ Aaron: _______ Geometry Name: ___________________________________ Unit 6 WS 6 (Proportions) Date: ____________________________________ Directions: Solve each proportion. 1. 5. x 6 2 12 2 3x 5 7 2. 3 9 5 x 3. 2x 12 5 15 4. 8 2 x 5 6. x 5 1 4 2 7. x 3 4 2 3 8. x 4 7 2 9. x 2 4 x 3 5 10. x 3 2x 1 2 3 11. x 4 6 x 4 5 12. 3x 5 18x 5 3 7 Geometry Name: ___________________________________ Unit 6 WS 6 (Proportion Apps) Date: ____________________________________ Directions: Solve each proportion word problem. Show all work; label all answer. 1. If 6 pounds of apples cost $9, then how much would 21 pounds of apples cost? Answer: ______________ 3. If $24 worth of fertilizer covers 5,000 square feet, then how much would it cost to cover 30,000 square feet? 2. The scale on a map is 1 inch equals 5 feet. What is the distance between two points on the map that are 8 1/2 inches apart on the map? Answer: ______________ 4. If a chain link fence costs $180 for 20 feet installed, how much would it cost to install 300 feet? Answer: ______________ Answer: ______________ 5. A store makes a profit of $15,000 for every 300 coats that they sell. If they make a profit of $25,000, how many coats did they sell? 6. Last week you earned $262.90 after working 22 hours. How much will you earn this week if you have worked 15 hours. Answer: ______________ Answer: ______________ Geometry Name: __________________________ Unit 6 – Similarity Date: ___________________________ Similarity: _____________________________________________________________ ______________________________________________________________________ 1. __________________________________________________________ ____________________________________________________________ 2. __________________________________________________________ ____________________________________________________________ The symbol for similarity is: _______. Example 1: Ex2. If ABCD ~ WXYZ, then… A @ _______ B @ __________ C @ _______ D @ __________ AB BC CD DA page 9 Geometry Name: __________________________ Unit 6 – Similarity Date: ___________________________ Ex3. If DDOG ~ DCAT, then all corresponding angles are congruent. Also, all sides are in proportion (share the same scale factor). The scale factor of DDOG to DCAT is ___________. In other words, all of the corresponding sides will form ratios equivalent to ___________. Name the similar figures. Ex4. Ex5. page 10 Geometry Name: __________________________ Unit 6 – Similarity Date: ___________________________ Example 6 – Find the missing side lengths and angle measures. DABC ~ _________ Scale Factor: Example 7 – Find the missing side lengths and angle measures. page 11 Geometry Name: __________________________ Unit 6 WS 7 Date: ___________________________ Determine whether the figures are similar. If so, name the similarity relationship and the scale factor. Example E A 26 10 12 20 B 5 D 1. 70 15 B 6 13 E F 6 D 15 10 C F Yes 4 10 C 24 A H G 4 Scale Factor: 2 to 1 DABC ~ DDEF 2. J 6 K Q 5 P 3 8 R 6 M L 65 6 H 55 125 115 4 7 T A G T 18 80 A 80 110 27 75 C 110 D G 165 80 55 R 12 8 F 21 B 165 6 E 115 14 T 6 125 12 I 80 W 20 U 5. 65 14 80 80 O 5 S 9 4 21 21 8 M V 20 3 N 4. 3. J 74 110 111 16 I H Geometry Name: __________________________ Unit 6 WS 7 Date: ___________________________ In each problem the figures shown are similar. Name the similar figures; identify the scale factor; find all missing side lengths and angle measures indicated by variables. Show work. 1. z 35 18 21 85 D T Q 15 8 y 12 A 2. F B 60 P C 18 15 S E x x z y 80 U R 14 y is a decimal. Figures: ___________________________ Figures: ___________________________ Scale Factor: _______________________ Scale Factor: _______________________ x = ______ x = ______ 3. A y = ______ 16 z = ______ E B y x H 10 G x 9 M z = ______ N z 12 15 D 4. F y = ______ 60 O z Y 12 y 8 C 24 X 60 50 Z 16 x and y are decimals. Figures: ___________________________ Figures: ___________________________ Scale Factor: _______________________ Scale Factor: _______________________ x = ______ x = ______ y = ______ z = ______ y = ______ z = ______ Geometry Name: __________________________ Unit 6 WS 8 Date: ___________________________ In each problem the figures shown are similar. Name the similar figures; identify the scale factor; find all missing side lengths and angle measures indicated by variables. 1. A 2. K 18 12 z y E G F E H 12 5 10 H 15 D 12 M z y B 2.5 J G 10 L x K F 3 J x C Figures: ___________________________ Figures: ___________________________ Scale Factor: _______________________ Scale Factor: _______________________ x = ______ x = ______ y = ______ 3. D A y z = ______ E 4. z C 15 D 40 22 70 50 z = ______ B 30 12 F y 110 x 15 A y = ______ F C 30 70 40 x B G z w E 110 12 H Figures: ___________________________ Figures: ___________________________ Scale Factor: _______________________ x = ______ y = ______ z = ______ Scale Factor: _______________________ w = _____ x = _____ y = _____ z = ____ What kind of quadrilaterals are these figures? ___________________________