TODAY IN GEOMETRY… Review: Arc Length Learning Target : 11.3 You will use ratios to find areas of similar figures Independent practice CH.10 TEST – THURSDAY/FRIDAY!

REVIEW: Find 𝑚𝐶𝐵 Arc is twice the inscribed arc. 2. Angles around a circle add to 360° 6𝑥+20+17+7𝑥+2 5𝑥−11 =𝟑𝟔𝟎 6𝑥+20+17+7𝑥+10𝑥−22=360 23𝑥+15=360 − 15 − 15 23𝑥=345 23 23 𝒙=𝟏𝟓 3. 𝑚𝐶𝐵=6𝑥+20 2(5𝑥−11) =6 15 +20 =𝟏𝟏𝟎°

AREAS OF SIMILAR POLYGONS: 𝑃𝑜𝑙𝑦𝑔𝑜𝑛 𝐼~𝑃𝑜𝑙𝑦𝑔𝑜𝑛 𝐼𝐼 𝑏 𝑎 Polygon I Polygon II POLYGON I 𝑎 RATIO OF SIDES: = POLYGON II 𝑏 POLYGON I 𝑎 RATIO OF PERIMETERS: = POLYGON II 𝑏 POLYGON I 𝑎 2 RATIO OF AREAS: = POLYGON II 𝑏 2

EXAMPLE: In the diagram, ∆𝐴𝐵𝐶~∆𝐷𝐸𝐹. Find the indicated ratio. Ratio (red to blue) of the perimeters of the areas 8 = 2 3 a. Ratio of Perimeter = 12 2 2 = 4 9 b. Ratio of Areas = 3 2

PRACTICE: In the diagram, 𝐹𝑖𝑔𝑢𝑟𝑒 1~𝐹𝑖𝑔𝑢𝑟𝑒 2. Find the indicated ratio. Ratio of the perimeters Ratio of the areas 18 10 Figure 1 Figure 2 18 = 9 5 a. Ratio of Perimeter = 10 9 2 = 81 25 b. Ratio of Areas = 5 2

EXAMPLE: Rectangles I and II are similar EXAMPLE: Rectangles I and II are similar. The perimeter of Rectangle I is 66 inches. Rectangle II has a perimeter of 110 inches and an area of 700 𝑖𝑛 2 . Find the area of Rectangle I. 66 = 3 5 Ratio of Perimeter = 𝑅𝑒𝑐𝑡𝑎𝑛𝑔𝑙𝑒 𝐼 𝑅𝑒𝑐𝑡𝑎𝑛𝑔𝑙𝑒 𝐼𝐼 = Ratio of Areas = 𝑅𝑒𝑐𝑡𝑎𝑛𝑔𝑙𝑒 𝐼 𝑅𝑒𝑐𝑡𝑎𝑛𝑔𝑙𝑒 𝐼𝐼 = Set up proportions of areas = Cross multiply 25𝑥=9(700) 25𝑥=6300 Divide 25 25 𝒙=𝟐𝟓𝟐 𝒊𝒏 𝟐 110 3 2 = 9 25 5 2 9 𝑥 25 700

EXAMPLE 2: Find the ratio of the perimeter (red to blue) and area EXAMPLE 2: Find the ratio of the perimeter (red to blue) and area. Then find the unknown area. 12𝑓𝑡 𝐴=64 𝑓𝑡 2 16𝑓𝑡 16 = 4 3 Ratio of Perimeter = 𝑟𝑒𝑑 𝑏𝑙𝑢𝑒 = Ratio of Areas = 𝑟𝑒𝑑 𝑏𝑙𝑢𝑒 = Set up proportions of areas = Cross multiply 9(64)=16𝑥 576=16𝑥 Divide 16 16 𝒙=𝟑𝟔 𝒇𝒕 𝟐 12 4 2 = 16 9 3 2 16 64 9 𝑥

PRACTICE: Find the ratio of the perimeter (red to blue) and area PRACTICE: Find the ratio of the perimeter (red to blue) and area. Then find the unknown area. 10𝑓𝑡 14𝑓𝑡 10 = 5 7 Ratio of Perimeter = 𝑟𝑒𝑑 𝑏𝑙𝑢𝑒 = Ratio of Areas = 𝑟𝑒𝑑 𝑏𝑙𝑢𝑒 = Set up proportions of areas = Cross multiply 49𝑥=25(441) 49𝑥=11025 Divide 49 49 𝒙=𝟐𝟐𝟓 𝒇𝒕 𝟐 𝐴=441 𝑓𝑡 2 14 5 2 = 25 49 7 2 25 𝑥 49 441

PRACTICE: Find the ratio of the perimeter (red to blue) and area PRACTICE: Find the ratio of the perimeter (red to blue) and area. Then find the unknown area. 𝐴=108 𝑓𝑡 2 12𝑓𝑡 8𝑓𝑡 12 = 3 2 Ratio of Perimeter = 𝑟𝑒𝑑 𝑏𝑙𝑢𝑒 = Ratio of Areas = 𝑟𝑒𝑑 𝑏𝑙𝑢𝑒 = Set up proportions of areas = Cross multiply 4(108)=9𝑥 432=9𝑥 Divide 9 9 𝒙=𝟒𝟖 𝒇𝒕 𝟐 8 3 2 = 9 4 2 2 9 108 4 𝑥

HOMEWORK #10: Pg. 740: 3-14 If finished, work on other assignments: HW #1: Pg. 655: 3-20, 24-26, 30 HW #2: Pg. 661: 3-14, 17, 23 HW #3: Pg. 667: 3-15 HW #4: Pg. 676: 3-16 Pg. 679: 40-46 HW #5: Pg. 683: 3-13 HW #6: Pg. 692: 3, 4, 6, 9-14 HW #7: Pg. 702: 3-25 HW #8: Pg. 749: 3-7, 11-13, 15-23 HW #9: Pg. 758: 11-17, 26-31