If a series of rigid transformations maps ∠F onto ∠C where ∠F is congruent to ∠C, then which of the following statements is true? a. ΔABC ~ ΔFDE because of the definition of similarity in terms of similarity transformations
b. ΔABC ~ ΔFDE because of the AA similarity postulate
c. segment BC ~ segment EF because of the definition of similarity in terms of similarity transformations
d. segment BC ~ segment EF because corresponding parts of similar triangles are similar

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Step-by-step explanation:

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

in simplified version   it would be x ≤-4

step-by-step explanation:

multiply each term in x ≤-4 by -1