A square has four interior angles, each measuring 90°. All four sides of the square are equal in length, and the opposite sides are parallel to each other. The diagonals of the square bisect one another at a right angle (90°) and are equal in length. A square has four vertices and four sides, and its diagonals divide the square into two congruent isosceles triangles. Additionally, the length of the diagonals is greater than the length of its sides.

A rectangle is a quadrilateral with opposite sides that are parallel and equal in length. Each of its interior angles measures 90 degrees, and the sum of all interior angles is 360 degrees. The diagonals of a rectangle bisect each other and are equal in length. For a rectangle with side lengths aaa and bbb, the perimeter is given by 2a+2b2a + 2b2a+2b units, and the area is ababab square units. The diagonals serve as the diameters of the rectangle’s circumcircle, and their length is determined using the formula a2+b2\sqrt{a^2 + b^2}a2+b2​. The diagonals intersect at different angles—one acute and the other obtuse. If the diagonals bisect each other at right angles, the rectangle becomes a square. When a rectangle is rotated along the line joining the midpoints of its longer parallel sides, a cylinder is formed. In this case, the height of the cylinder equals the width of the rectangle, and the cylinder's diameter corresponds to the length of the rectangle. Similarly, if the rectangle is rotated along the line joining the midpoints of its shorter parallel sides, the height of the cylinder equals the length of the rectangle, and the diameter is equal to the width of the rectangle.

Circles are considered congruent if they have the same radius. The diameter of a circle is its longest chord. Chords of equal length in a circle subtend equal angles at the center, and a radius drawn perpendicular to a chord bisects that chord. Circles with different radii are similar. A circle can circumscribe shapes such as a rectangle, trapezium, triangle, square, or kite, and it can also be inscribed within a square, triangle, or kite. Chords that are equidistant from the center of a circle are equal in length, and the distance from the center to the diameter, the longest chord, is zero. As the length of a chord increases, the perpendicular distance from the center decreases. Tangents drawn at the ends of the diameter are parallel to each other. An isosceles triangle is formed when the radii connect the ends of a chord to the center of the circle.

The angles of any triangle, regardless of type, always add up to 180°. The sum of the lengths of any two sides of a triangle is greater than the length of the third side, and the difference between the lengths of two sides is less than the length of the third side. In a triangle, the side opposite the largest angle is the longest. The exterior angle of a triangle is equal to the sum of its two interior opposite angles, a relationship known as the exterior angle property. Two triangles are considered similar if their corresponding angles are congruent and their sides are proportional in length. The area of a triangle is calculated using the formula ½ × base × height, and its perimeter is the sum of the lengths of all three sides.

A square has four interior angles, each measuring 90°. All four sides of the square are equal in length, and the opposite sides are parallel to each other. The diagonals of the square bisect one another at a right angle (90°) and are equal in length. A square has four vertices and four sides, and its diagonals divide the square into two congruent isosceles triangles. Additionally, the length of the diagonals is greater than the length of its sides.