How to turn a square into a triangle: put four small triangles at the four corners of the square and the other four small triangles at the midpoint of the four sides of the square, and that's it.

First, the mathematical concept of square

A square is a special parallelogram. That is, a group of parallelograms with equal adjacent sides and a right angle is called a square, also known as a regular quadrilateral. A square has all the characteristics of a rectangle and a diamond.

Second, the definition

A parallelogram with a right angle and a set of equal adjacent sides is a square.

Third, the decision theorem

1, the rhombus with equal diagonal lines is a square.

2. Diamonds with right angles are squares.

3. A rectangle with diagonal lines perpendicular to each other is a square.

4. A set of rectangles with equal adjacent sides is a square.

5. A set of parallelograms with equal adjacent sides and a right angle is a square.

6. A parallelogram with vertical and equal diagonals is a square.

7. A quadrilateral with equal diagonal and median perpendicular is a square.

8. A set of quadrilaterals with equal adjacent sides and three right angles is a square.

9. A quadrilateral that is both a diamond and a rectangle is a square.

Fourth, nature.

1, edge: two groups of opposite edges are parallel respectively; All four sides are equal; Adjacent sides are perpendicular to each other.

2. Internal angle: All four angles are 90, and the sum of internal angles is 360.

3. Diagonal lines: Diagonal lines are perpendicular to each other; Diagonal lines are equal and equally divided; Each diagonal bisects a set of diagonal lines.

4. Symmetry: it is both a central symmetrical figure and an axisymmetric figure (with four axes of symmetry).

5. Special properties: a diagonal line of a square divides the square into two isosceles right triangles, and the included angle between the diagonal line and the side is 45; The two diagonal lines of a square divide it into four congruent isosceles right-angled triangles.

6. Other properties: A square has all the properties and characteristics of parallelogram, rhombus and rectangle.

7. Other properties: Draw the largest circle in the square (inscribed circle of the square), and the area of this circle is about 78.5% [4 π] of the square area; The area of the smallest circle (circumscribed circle of a square) that completely covers a square is about 157% [π] of the square area.

8. Other properties: A square is a special rectangle and a square is a special diamond.