Can someone please help write a proof for the following.

given: JKLM is a square
prove: MK is perpendicular to LJ

the figure in front of me is a square labeled JKLM and there are diagonals JL and KM

We are not going to write the proof for you. It is outlined here..

http://www.jiskha.com/display.cgi?id=1301521089

To prove that MK is perpendicular to LJ in the square JKLM, we can follow these steps:

1. Recall the properties of a square: all sides are equal in length, and the diagonals bisect each other at right angles.

2. Given that JKLM is a square, we know that JL and KM are its diagonals.

3. Since JL and KM are diagonals of a square, they bisect each other. This means that the point where they intersect, denoted as point N, is the midpoint for both diagonals.

4. Let's denote point N as the midpoint of JL and KM. We can then label the lengths of NJ, NK, and NM as a, b, and c, respectively.

5. By the midpoint property, we can assert that NJ = JL / 2 = a/2 and NK = KL / 2 = b/2.

6. Now, we can examine the right triangles JNK and KMN.
- In triangle JNK, we have a right angle at angle JNK since JKLM is a square. Therefore, angle JNM is also right.
- In triangle KMN, we can deduce that angle NMK is also right for the same reason.

7. Combining the information from steps 5 and 6, we find that JNM and MNK are right angles. Therefore, by definition, MK is perpendicular to LJ.

This completes the proof that MK is perpendicular to LJ in the square JKLM.