1. 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!

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

3. 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

4. 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

5. 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

6. 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 𝑥=9(700)
25𝑥=6300
Divide
𝒙=𝟐𝟓𝟐 𝒊𝒏 𝟐
110
3 2
= 9 25
5 2 9 𝑥 25
700

7. 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
𝒙=𝟑𝟔 𝒇𝒕 𝟐 12
4 2
= 16 9
3 2 16 64 9 𝑥

8. 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 𝑥=25(441)
49𝑥=11025
Divide
𝒙=𝟐𝟐𝟓 𝒇𝒕 𝟐
𝐴=441 𝑓𝑡 2 14
5 2
= 25 49
7 2 25 𝑥 49
441

9. 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
𝒙=𝟒𝟖 𝒇𝒕 𝟐 8
3 2
= 9 4
2 2 9
108 4 𝑥

10. 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