Given: Rectangle ABCD with coordinates A(0, 0),

B(0, 8), C(5, 8), and D(5, 0). E is mdpt. of BC, and
F is mdpt. of AD.
Prove: EF = AB

Did you sketch it ?

AB= √(0^2 + 8^2) = 8

F is (5/2,8)
E is (5/2, 0)

FE = √( (5/2-5/2)^2 + (8-0)^2 )
= √(0 + 64) = 8

so AB = EF

To prove that EF = AB, we need to show that the length of segment EF is equal to the length of segment AB. Here's how we can do that:

1. Find the coordinates of points E and F:
- Point E is the midpoint of line segment BC.
- Point F is the midpoint of line segment AD.

2. Calculate the length of segment EF:
- Use the distance formula to find the distance between points E(xE, yE) and F(xF, yF).
- The distance formula is given by:
distance = sqrt((xF - xE)^2 + (yF - yE)^2).

3. Calculate the length of segment AB:
- Use the distance formula to find the distance between points A(xA, yA) and B(xB, yB).

4. Compare the length of segment EF with the length of segment AB:
- If EF = AB, then the lengths are equal, and the proof is complete.
- If EF ≠ AB, then the lengths are not equal, and the proof is unsuccessful.

By following these steps and performing the necessary calculations, we can determine whether EF is equal to AB in the given rectangle.