How to write a proof for a square.

[paradiselovekiss]

Hello, I need help on how to write a proof proving that the diagonals of a square are perpendicular. Please help for my math test is coming soon thank you. ^^
I'm sorry I can't figure out how to post a picture on here so this is the description of my square:
1. The square name ABCD
2. Have a diagnol inside the square from A to C and B to D

This is what I have so far:
1.ABCD is a square 1. Given
2. segment AB is 2. Square have all congruence sides
congruence to segment AD
; Segment BC is congruence
to segment CD 3. Reflecsive
3. Segment AC is congruence
to segment AC.
4. Triangle ABC is congruence 4. SSS
to triangle ADC
5. Angle AEB is congruence 5. Congruence parts of congruence triangle are congruence
to angle CED


Please help me thank you SO MUCH.

 

[soroban]

Hello, paradiselovekiss!

I have a simpler proof.
I hope it's acceptable in your course.

    A               B
      * - - - - - *
      | *       * |
      |   *   *   |
      |     *     |
      |   *   * - |
      | *       * |
      * - - - - - *
    D               C

There is a theorem that says:
. . Two points equidistant from the endpoints of a line segment
. . determine the perpendicular bisector of the line segment.


\(\displaystyle AB = AD,\;\;CB =CD\qquad\text{(The sides of a square are equal.)}\)

\(\displaystyle A\text{ is equidistant from }B \text{ and }D.\)
\(\displaystyle C\text{ is equidistant from }B\text{ and }D.\)

\(\displaystyle \text{Hence, }AC\text{ is the }perpendicular\text{ bisector of }BD.\)

\(\displaystyle \text{Therefore: }\:AC \perp BD\)