SIMILAR TEST REVIEW STUDY, STUDY, STUDY!!!

HOW CAN A RATIO BE WRITTEN?

HOW CAN A RATIO BE WRITTEN? a : b and a/b

HOW CAN A RATIO BE WRITTEN? a : b and a/b READS: A TO B

What is the definition of a PROPORTION?

What is the definition of a PROPORTION? is an equation showing that two ratios are EQUAL to each other.

WHAT PROPERTIES AND THEOREMS ARE USED FOR PROVING SIMILAR TRIANGLES?

WHAT PROPERTIES AND THEOREMS ARE USED FOR PROVING SIMILAR TRIANGLES? AA SSS SAS

SOLVING PROPORTIONS 1. 10 𝑘 = 8 4 2. 1 𝑥 − 9 = 9 99

SOLVING PROPORTIONS 1. 10 𝑘 = 8 4 2. 1 𝑥 − 9 = 9 99 10(4) = 8(k) CROSS-MULTIPLY 1(99) = 9(X – 9)

SOLVING PROPORTIONS 1. 10 𝑘 = 8 4 2. 1 𝑥 − 9 = 9 99 10(4) = 8(k) CROSS-MULTIPLY 1(99) = 9(X – 9) 40 = 8K MULTIPLY TERMS 99 = 9X - 81

SOLVING PROPORTIONS 20 = X 1. 10 𝑘 = 8 4 2. 1 𝑥 − 9 = 9 99 1. 10 𝑘 = 8 4 2. 1 𝑥 − 9 = 9 99 10(4) = 8(k) CROSS-MULTIPLY 1(99) = 9(X – 9) 40 = 8K MULTIPLY TERMS 99 = 9X - 81 40 8 = 8K 8 SOLVE FOR X 99=9X −81 +81 +81 5 = K 180 = 9X 180 9 = 9X 9 20 = X

SETTING UP PROPORTIONS 80 60 40 x

SETTING UP PROPORTIONS Match the sides correctly. When not given the name of the triangles, then use either of these proportion. 𝐬𝐢𝐝𝐞 𝐛𝐚𝐬𝐞 𝐨𝐫 𝐬𝐢𝐝𝐞𝟏 𝐬𝐢𝐝𝐞𝟐 80 60 40 x

SETTING UP PROPORTIONS Match the sides correctly. When not given the name of the triangles, then use either of these proportion. 𝐬𝐢𝐝𝐞 𝐛𝐚𝐬𝐞 𝐨𝐫 𝐬𝐢𝐝𝐞𝟏 𝐬𝐢𝐝𝐞𝟐 In this case, what will we use? 80 60 40 x

SETTING UP PROPORTIONS Match the sides correctly. When not given the name of the triangles, then use either of these proportion. 𝐬𝐢𝐝𝐞 𝐛𝐚𝐬𝐞 𝐨𝐫 𝐬𝐢𝐝𝐞𝟏 𝐬𝐢𝐝𝐞𝟐 In this case, what will we use? 𝐬𝐢𝐝𝐞 𝐛𝐚𝐬𝐞 So plug it in, 80 60 40 x

SETTING UP PROPORTIONS Match the sides correctly. When not given the name of the triangles, then use either of these proportion. 𝒍𝒂𝒓𝒈𝒆 𝒕𝒓𝒊𝒂𝒏𝒈𝒍𝒆 𝒔𝒎𝒂𝒍𝒍 𝒕𝒓𝒊𝒂𝒏𝒈𝒍𝒆 Put the short sides together and the long sides together or 𝐬𝐢𝐝𝐞𝟏 𝐨𝐟 𝐥𝐚𝐫𝐠𝐞 𝐭𝐫𝐢𝐚𝐧𝐠𝐥𝐞 𝐬𝐢𝐝𝐞𝟐 𝐨𝐟 𝐥𝐚𝐫𝐠𝐞 𝐭𝐫𝐢𝐚𝐧𝐠𝐥𝐞 = 𝐬𝐢𝐝𝐞𝟏 𝐨𝐟 𝐬𝐦𝐚𝐥𝐥 𝐭𝐫𝐢𝐚𝐧𝐠𝐥𝐞 𝐬𝐢𝐝𝐞𝟐 𝐨𝐟 𝐬𝐦𝐚𝐥𝐥 𝐭𝐫𝐢𝐚𝐧𝐠𝐥𝐞 In this case, what will we use? So plug it in, long side large long side small = short side large short side small 80 40 = 60 x Cross-multiply and solve for x 80 60 40 x

SETTING UP PROPORTIONS 𝟖𝟎 𝟔𝟎 = 𝟒𝟎 𝐱 80(x) = 60(40) 80x = 2400 x = 30 80 60 40 x

PROVING TRIANGLES ARE SIMILAR Remember the 3 properties we use for similar triangles. AA SAS SSS When solving for questions like this, make sure the ratios equal each other. Don’t guess.

PROVING TRIANGLES ARE SIMILAR Which similarity theorem or postulate proves the triangles similar? 2 48o 12 12 52o 5 5 48o 4 9 9 52o 10 3

EXAMPLES Use the information in the figure shown below to find the length of x. 30 x 50 80

(Must make sure you keep corresponding parts together!!!!) EXAMPLES Use the information in the figure shown below to find the length of x. 40 Use Pythagoren Theorem to find missing side of smaller triangle 502 – 302 = 402 (Must make sure you keep corresponding parts together!!!!) 30 x 50 80

EXAMPLES Use the information in the figure shown below to find the length of x. Set up proportion: 𝟓𝟎 𝒙 = 𝟒𝟎 𝟖𝟎 30 x 50 80

EXAMPLES Use the information in the figure shown below to find the length of x. Set up proportion: 𝟓𝟎 𝒙 = 𝟒𝟎 𝟖𝟎 Solve for x: 30 x 50 80

EXAMPLES Use the information in the figure shown below to find the length of x. Set up proportion: 𝟓𝟎 𝒙 = 𝟒𝟎 𝟖𝟎 Solve for x: 50(80) = 40x x = 100 30 x 50 80

EXAMPLES Use the information in the figure shown below to find the length of x. The two triangles are similar. 40 x 60 180

EXAMPLES Use the information in the figure shown below to find the length of x. The two triangles are similar. Set up proportion: 40 x 60 180

EXAMPLES Use the information in the figure shown below to find the length of x. The two triangles are similar. Set up proportion: 𝟔𝟎+𝟒𝟎 𝟏𝟖𝟎 = 𝟒𝟎 𝒙 40 x 60 180

EXAMPLES Use the information in the figure shown below to find the length of x. The two triangles are similar. Set up proportion: 𝟔𝟎+𝟒𝟎 𝟏𝟖𝟎 = 𝟒𝟎 𝒙 Solve for x: 40 x 60 180

EXAMPLES Use the information in the figure shown below to find the length of x. The two triangles are similar. Set up proportion: 𝟔𝟎+𝟒𝟎 𝟏𝟖𝟎 = 𝟒𝟎 𝒙 Solve for x: 100x = 180(40) 40 x 60 180

EXAMPLES Use the information in the figure shown below to find the length of GJ. The two triangles are similar. J 100 R x G H 90 S 180

EXAMPLES Use the information in the figure shown below to find the length of GJ. The two triangles are similar. Set up proportion: J 100 R x G H 90 S 180

EXAMPLES Use the information in the figure shown below to find the length of GJ. The two triangles are similar. Set up proportion: 𝟗𝟎 𝒙 = 𝟏𝟖𝟎 𝒙+𝟏𝟎𝟎 J 100 R x G H 90 S 180

EXAMPLES Use the information in the figure shown below to find the length of GJ. The two triangles are similar. Set up proportion: 𝟗𝟎 𝒙 = 𝟏𝟖𝟎 𝒙+𝟏𝟎𝟎 Solve for x: J 100 R x G H 90 S 180

EXAMPLES Use the information in the figure shown below to find the length of GJ. The two triangles are similar. Set up proportion: 𝟗𝟎 𝒙 = 𝟏𝟖𝟎 𝒙+𝟏𝟎𝟎 Solve for x: 90 (x + 100) = 180(x) J 100 R x G H 90 S 180

PROVING TRIANGLES ARE SIMILAR Which graph below correctly shows ΔGHJ ~ ΔLMN WITH 𝑮𝑯 𝑳𝑴 = 𝟏 𝟐 ? N J J 2 20 H G 5 H 6 N G N L M 15 J L 4 12 18 M L G H M 10 5

EXAMPLE A large ad in the newspaper is 12 cm by 18cm. The next smallest size is reduced by a scale factor of 2/3. What is the size of the reduced ad?

EXAMPLE A large ad in the newspaper is 12 cm by 18cm. The next smallest size is reduced by a scale factor of 2/3. What is the size of the reduced ad? Set up ratio of large ad:

EXAMPLE A large ad in the newspaper is 12 cm by 18cm. The next smallest size is reduced by a scale factor of 2/3. What is the size of the reduced ad? Set up ratio of large ad: 12 18

EXAMPLE A large ad in the newspaper is 12 cm by 18cm. The next smallest size is reduced by a scale factor of 2/3. What is the size of the reduced ad? Set up ratio of large ad: 12 18 Multiply ratio by the scale factor:

EXAMPLE A large ad in the newspaper is 12 cm by 18cm. The next smallest size is reduced by a scale factor of 2/3. What is the size of the reduced ad? Set up ratio of large ad: 12 18 Multiply ratio by the scale factor: 12 18 × 2 3

EXAMPLE A large ad in the newspaper is 12 cm by 18cm. The next smallest size is reduced by a scale factor of 2/3. What is the size of the reduced ad? Set up ratio of large ad: 12 18 Multiply ratio by the scale factor: 12 18 × 2 3 = 12 54 2 9

EXAMPLE A flag is 6 feet by 12 feet, and is made into a bigger flag measured 21 feet by 42 feet. What is the scale factor used to enlarge the flag? A) 2/1 B) 7/2 C) 2/7 D) 7

EXAMPLE A flag is 6 feet by 12 feet, and is made into a bigger flag measured 21 feet by 42 feet. What is the scale factor used to enlarge the flag? A) 2/1 B) 7/2 C) 2/7 D) 7 Get your original ratio:

EXAMPLE A flag is 6 feet by 12 feet, and is made into a bigger flag measured 21 feet by 42 feet. What is the scale factor used to enlarge the flag? A) 2/1 B) 7/2 C) 2/7 D) 7 Get your original ratio: 6 12

EXAMPLE A flag is 6 feet by 12 feet, and is made into a bigger flag measured 21 feet by 42 feet. What is the scale factor used to enlarge the flag? A) 2/1 B) 7/2 C) 2/7 D) 7 Get your original ratio: 6 12 Multiply the answer choices to the ratio: (Reminder: Multiply the scale factor to both the numerator and the denominator)

EXAMPLE A flag is 6 feet by 12 feet, and is made into a bigger flag measured 21 feet by 42 feet. What is the scale factor used to enlarge the flag? A) 2/1 B) 7/2 C) 2/7 D) 7 Get your original ratio: 6 12 Multiply the answer choices to the ratio: (Reminder: Multiply the scale factor to both the numerator and the denominator) 2 1 × 6 12 = 7 2 × 6 12 = 2 7 × 6 12 = 7 1 × 6 12 =

EXAMPLE A flag is 6 feet by 12 feet, and is made into a bigger flag measured 21 feet by 42 feet. What is the scale factor used to enlarge the flag? A) 2/1 B) 7/2 C) 2/7 D) 7 Get your original ratio: 6 12 Multiply the answer choices to the ratio: (Reminder: Multiply the scale factor to both the numerator and the denominator) 2 1 × 6 12 = 12 24 ≠ 21 42 7 2 × 6 12 = 21 42 = 21 42 2 7 × 6 12 = 42 21 ≠ 21 42 7 1 × 6 12 = 42 84 ≠ 21 42