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. Ex4. Ex3. Ex5.

Where else do we see ratios and proportions? ______________________________________________________________________ Example: ______________________________________________________________ ______________________________________________________________________ Geometry Name: __________________________ Unit 6 – Similarity Date: ___________________________ 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

Geometry Name: ___________________________________ Unit 6 WS 5 (Ratio Apps)Date: ____________________________________ Directions: Solve each word problem. Show all work; label all answers 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. m  1 = _______ m  2 = _______ m  3 = _______ m  4 = _______ 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. First: __________ Second: ________ Third: _________ Fourth: ________ Fifth: __________ The ratio of two complementary angles is 2:3. Find the measure of each angle. m  1 = _______ m  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. The ratio of two supplementary angles is 4:5. Find the measure of each angle. 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. m  1 = _______ m  2 = _______ m  3 = _______ m  4 = _______ m  5 = _______ m  6 = _______ m  1 = _______ m  2 = _______ Adam: _______ Alan: ________ Aaron: _______

Geometry Name: ___________________________________ Unit 6 WS 6 (Proportions)Date: ____________________________________ Directions: Solve each proportion

Geometry Name: ___________________________________ Unit 6 WS 6 (Proportion Apps)Date: ____________________________________ Directions: Solve each proportion word problem. Show all work; label all answer If 6 pounds of apples cost $9, then how much would 21 pounds of apples cost? 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? If $24 worth of fertilizer covers 5,000 square feet, then how much would it cost to cover 30,000 square feet? If a chain link fence costs $180 for 20 feet installed, how much would it cost to install 300 feet? 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? Answer: ______________ Last week you earned $ after working 22 hours. How much will you earn this week if you have worked 15 hours.

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   page 9

Geometry Name: __________________________ Unit 6 – Similarity Date: ___________________________ Ex3. Ex4.Ex5. If  DOG ~  CAT, then all corresponding angles are congruent. Also, all sides are in proportion (share the same scale factor). The scale factor of  DOG to  CAT is ___________. In other words, all of the corresponding sides will form ratios equivalent to ___________. Name the similar figures. page 10

Geometry Name: __________________________ Unit 6 – Similarity Date: ___________________________ Example 6 – Find the missing side lengths and angle measures.  ABC ~  Scale Factor: Example 7 – Find the missing side lengths and angle measures. page 11

Geometry Name: __________________________ Unit 6 WS 7Date: ___________________________ Determine whether the figures are similar. If so, name the similarity relationship and the scale factor. Example Yes Scale Factor: 2 to 1  ABC ~  DEF B A C F E D AB CD H EF G JK L M N QP O S T R V U W C DE A B G H IJ F 80  20   70  MA TH I T R G 65  55  65  125  115  125   75  165  80  110  111  74  165 

Geometry Name: __________________________ Unit 6 WS 7Date: ___________________________ 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 Figures: ___________________________ Scale Factor: _______________________ x = ______ y = ______ z = ______ Figures: ___________________________ Scale Factor: _______________________ x = ______ y = ______ z = ______ Figures: ___________________________ Scale Factor: _______________________ x = ______ y = ______ z = ______ Figures: ___________________________ Scale Factor: _______________________ x = ______ y = ______ z = ______ A B C D F E 18 x 8 12 y  z 85  P Q R S U T 60  80  x z y y is a decimal. N M O Y Z X x 9 8 y z 60  50  D AB C H EF G x y z 10 x and y are decimals. 60 

Geometry Name: __________________________ Unit 6 WS 8Date: ___________________________ 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 Figures: ___________________________ Scale Factor: _______________________ x = ______ y = ______ z = ______ Figures: ___________________________ Scale Factor: _______________________ x = ______ y = ______ z = ______ Figures: ___________________________ Scale Factor: _______________________ w = _____ x = _____ y = _____ z = ____ What kind of quadrilaterals are these figures? ___________________________ Figures: ___________________________ Scale Factor: _______________________ x = ______ y = ______ z = ______ EB DC AK G J H F y x z F E H G J L M K x z y A C B F ED y 15 z D AB C F E H G y x z 70  110  40  ww x