Question

The vertices of DEF are D(7, 3), E(4, -3), and F(10, -3) Write a paragraph proof to prove that DEF is isosceles.

Answer 1

DEF is isosceles because, E and F both have -3 for the y-axis therefore no matter what number the x-axis is they will still be equal

Answer 2

DEF is isosceles because we need first to calculate the length of each side.

In order to calculate the length between 2 points like (x1, y1) and (x2, y2), we have to use the next equation:

d = { (x1-x2)^2 + (y1-y2)^2 }^(1/2)

1) In this case the length between D and E is:

DE = { (7-4)^2 + (3-(-3))^2 }^(1/2) = square root of 45

2) In this case the length between E and F is:

EF = { (4-10)^2 + (-3-(-3))^2 }^(1/2) = 6

3) In this case the length between D and F is:

DF = { (7-10)^2 + (3-(-3))^2 }^(1/2) = square root of 45

In conclusion, as we can see DE = DF so this means that the DEF is isosceles.

Explanation: