How would you rate our town's library services? Do not use
Good
Average
Poor
library
Male Female Male Female
Male
Female Male Female
10 8 5 7
5
5 17 18
30 28 25 30 20 30
20 20
30 32 26 21 15 10 5 10
21 25 8 15 2. 10 2 5
91 93 644 73 12 55 44
Age (in years)
18-25
26-40
41-65
66 and older
Total
1.
Total
75
203
1-49
88
515
1
53
What is the probability that a person who rated the town's library services as "poor" is a
male?
46.8%
56.796
43.3%
18.8%

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)