The nature of parallelogram: the opposite sides are parallel and equal, the diagonal lines are equal, and the diagonal lines are equally divided. Determination of parallelogram: 1. A set of parallelograms with equal sides, 2. The quadrangles bisecting each other are parallelograms, 3. Two groups of parallelograms with equal opposite sides are parallelograms, and 4. Two groups of parallelograms with equal diagonals are parallelograms. The nature of a rectangle: the opposite sides are parallel and equal, the diagonal lines are equal, the four corners are right angles, the diagonal lines are equal, and they are equally divided. Judgment of rectangle: 1. Parallelograms with equal diagonals are rectangles; 2. Quadrilaterals with equal diagonals are rectangles; 3. A quadrilateral with three right angles is a rectangle; 4. A parallelogram with a right angle is a rectangle. The nature of the diamond: the opposite sides are parallel and equal, the four sides are equal, the diagonals are equally divided, and the two diagonals are equally divided into two groups of diagonals. Judgment of diamond: 1. A quadrilateral with four equilateral sides is a diamond, 2. The parallelogram with orthogonal diagonal lines is a diamond, 3. A quadrilateral with orthogonal diagonal lines is a diamond. The nature of a square: the opposite sides are parallel and equal, the four sides are equal, the four corners are right angles, the diagonals are equal and bisected vertically, and the two diagonals bisect two groups of diagonals. Judgment of a square: 1. A diamond with a right angle is a square, 2. A set of rectangles with equal adjacent sides is a square, 3. A diamond with equal diagonal lines is a square. A rectangle with orthogonal diagonal lines is a square. Diagonal line Properties of isosceles trapezoid: 1. The two base angles of the isosceles trapezoid on the same base are equal, and the two diagonal lines of the isosceles trapezoid are equal. Determination of isosceles trapezoid: A trapezoid with two equal angles on the same base is an isosceles trapezoid. Triangle midline theorem: the midline of a triangle is parallel to the third side and equal to half of the third side. Mean value theorem of trapezoid: the center line of trapezoid is parallel to two bottoms and equal to half of the sum of the two bottoms.