Show that the diagonals of a square are equal and bisect each other at right angles.

Explanation

To prove that the diagonals of a square are equal and bisect each other at right angles, we will follow a systematic approach. Let's denote the square as ABCD, where A, B, C, and D are the vertices of the square. The diagonals are AC and BD, and they intersect at point O.

### Step 1: Prove that the diagonals are equal.
1. **Identify the triangles**: Consider triangles AOD and BOC.
2. **Sides of the square**: Since ABCD is a square, all sides are equal. Thus, AD = BC.
3. **Common side**: The diagonal DC is common to both triangles AOD and BOC.
4. **Angles**: The angles at A and B are both right angles (90 degrees) because the angles in a square are right angles.
5. **Congruence**: By the Side-Angle-Side (SAS) criterion, triangles AOD and BOC are congruent.
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