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XY = 2 units

Step-by-step explanation:

Given that :

ΔEFG ≅ ΔXYZ

Then, segments :

EF = XY, FG = YZ and EG = XZ

GIVEN THAT :

E (0, 0), F (0, 2), and G (3, 0)

We can find the distance between coordinates E (0, 0), F (0, 2) to get the measure of XY since they are both congruent.

EF = sqrt[(x2 - x1)^2 + (y2 - y1)^2]

x1 = 0, y1= 0, x2 = 0, y2 = 2

EF = sqrt[(0 - 0)^2 + (2 - 0)^2]

EF = sqrt[ 0 + 4]

EF = 2

SINCE EF = XY

XY = 2 units