Determine if the following triangle is a right triangle or not using the Pythagorean Theorem Converse. Triangle with side lengths of: 8 in, 15 in and 17 in please answear.

It is a right triangle

Step-by-step explanation:

Information needed:

Formula: a^2+b^2= c^2

a: leg

b: leg

c: hypotenuse

the longest side is always the hypotenuse, so 17 in

the order of legs don't matter so 8 in and 15 in

Solve:

a^2+b^2= c^2

8^2+15^2= 17^2

64+225= 289

289= 289

Final

It is a right triangle

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.