Now select points B and C, and move them around. What do you notice about as you move B and C? What do you notice about the ratios of the lengths of the intersected segments as you move B and C?

As points B and C move, DE moves in such a way that it remains parallel to BC. The lengths of the segments change with B and C, but the ratios remain the same.

Step-by-step explanation:

Plato Answer

When points B and C move, DE moves yet it remains parallel to BC.

Lengths segments change with B and C: ratios remain the same.

Step-by-step explanation:

I changed up the sample answer same stuff just worded different so it is not put as plagiarism

the answer is simply just 6n add the two together as they have an n

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240