Why are the ratios DEAD and D′E′AD′ equal? Is the same true for the ratios
AEAD and AE′AD′?

because everyone's equal when they're dead!

Step-by-step explanation:

here's the thing about equality, everyone's equal when they're dead!

Below

Step-by-step explanation:

We want to prove that RS and UV have the same slope.

The coordinates of the four points:

● R(-2,7)

● S(-8,1)

● U(4,5)

● V(1,2)

Let's start by calculating the slope of RS.

Let m be the slope of RS:

● m=(7-1)/[-2-(-8)]= 6/(-2+8)=6/6 = 1

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Let's calculate the slope of UV

Let m' be the slope of UV

● m' = (2-5)/(1-4)= (-3)/(-3) = 1

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m = m' so UV and RS have the same slope.