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answer:

a. there is no proportional relationship

b. there is a proportional relationship

step-by-step explanation:

cross multiply:

a. 35 * 80 = 23 * 92  

simplifying

35 * 80 = 23 * 92  

multiply 35 * 80

2800 = 23 * 92  

multiply 23 * 92

2800 = 2116  

solving

2800 = 2116  

couldn't find a variable to solve for.  

this equation is invalid, the left and right sides are not equal, therefore there is no solution.

b.cross multiply:

20 * 5 = 12.5 * 8  

simplifying

20 * 5 = 12.5 * 8  

multiply 20 * 5

100 = 12.5 * 8  

multiply 12.5 * 8

100 = 100  

add '-100' to each side of the equation.

100 + -100 = 100 + -100  

combine like terms: 100 + -100 = 0

0 = 100 + -100  

combine like terms: 100 + -100 = 0

0 = 0  

solving

0 = 0    

this equation is an identity, all real numbers are solutions.

explanation:

previous steps have made pa≅ pb ≅ st ≅ su. setting the compass width to ab allows you to make tu the same length. then δstu ≅ δpab by the sss congruence postulate, and ∠p ≅ ∠s by the reason cpctc.