Look at the figure below:

triangle srp has measure of angle srp equal to 90 degrees. q is a point on the hypotenuse sp such that the segment qr is perpendicular to ps. t is a point outside the triangle on the left of s so that triangle qts has the measure of angle qts equal to 90 degrees.

which triangle is similar to triangle pqr?

triangle rqs
triangle qts
triangle stq
triangle spr

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.

4x and 6y

im not sure though

step-by-step explanation: