Questions answered
The diagram shows a larger square divided into a smaller square and four right triangles. The
diagram can be used to prove the Pythagorean theorem.
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Complete the proof of the Pythagorean theorem.
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The area of the larger square found by multiplying its side lengths is
The smaller
square has side lengths of a - b. The combined area of the four triangles and the smaller
square is
which is equivalent to a? - 2ab + b² + 2ab. a? - 2ab +
b2 + 2ab is also equivalent to
. This expression and the expression found by
multiplying the larger square's side lengths both represent the same area. Therefore,

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.

hi,

you half the rectangle that you ae asking about so then you would see the scale factor of 1/2 the one u have selected, the one on top is half.

hope this !