2. Quadrilaterals whose diagonals bisect each other are parallelograms.
3. A set of quadrilaterals with parallel and equal opposite sides is a parallelogram.
4. Two groups of quadrangles with equal diagonals are parallelograms.
5. Two groups of parallelograms with parallel opposite sides are parallelograms [Edit this paragraph] Property (1) The graph obtained by connecting the midpoints of any quadrilateral is a parallelogram.
(2) If the diagonal of the quadrilateral is equally divided,
Then the figure obtained by connecting the midpoints of this quadrilateral is a parallelogram.
(3) The diagonals of parallelogram are equal, and the two adjacent angles are complementary.
(4) Divide the parallelogram into two congruent parts by the straight line at the diagonal intersection of the parallelogram.
5] A parallelogram is a figure with a symmetrical center, and the symmetrical center is the intersection of two diagonals.
The area of a parallelogram is equal to the product of the base and the height. (It can be considered as a rectangle)
A set of parallelograms with equal adjacent sides is defined as a rhombus, and the diagonals are perpendicular to each other and divided into two.
All four sides are equal;
Diagonal angles are equal and adjacent angles are complementary;
Each diagonal bisects a set of diagonal lines,
The diamond is not only an axisymmetric figure, but also a straight line with two diagonal lines, and it is a centrally symmetric figure.
60 rhombus, the short diagonal is equal to the side length, and the long diagonal is √3 times of the short diagonal.
A diamond has all the characteristics of a parallelogram. [Edit this paragraph] Make sure that a group of parallelograms with equal adjacent sides are diamonds.
A quadrilateral with four equilateral sides is a diamond.
Two quadrangles with diagonal symmetry are diamonds.
A quadrilateral whose diagonals are perpendicular to each other and split in two is a diamond.
The quadrilateral obtained by connecting the midpoints of the sides of the quadrilateral in turn is called the midpoint quadrilateral. No matter how the shape of the original quadrangle changes, the shape of the midpoint quadrangle is always a parallelogram. The midpoint quadrangle of a rhombus is a rectangle (the midpoint quadrangle of a quadrangle with vertical diagonal lines is a rectangle), and the midpoint quadrangle of a quadrangle with equal diagonal lines is a rhombus.
A diamond is defined on the premise of a parallelogram. First of all, it is a parallelogram, but it is a special parallelogram, which is characterized by "a group of adjacent sides are equal", thus adding some special properties and judgment methods different from parallelogram.
Diamonds are centrally symmetric figures. [Edit this paragraph] Defining a parallelogram with right angles is called a rectangle. It is a rectangle. [Edit this paragraph] Property 1. The four corners of a rectangle are right angles and the opposite sides are equal.
2. The diagonals of rectangles are equal.
3. The sum of squares of the distances from any point on the rectangular plane to its two diagonal endpoints is equal.
4. A rectangle is both an axisymmetric figure and a centrally symmetric figure (the symmetry axis is a line connecting the midpoints of any group of opposite sides).
5. The opposite sides are parallel and equal
6. Divide diagonally.
7. A rectangle has all the properties of a parallelogram [edit this paragraph]. Judge 1. A parallelogram with right angles is a rectangle.
2. Parallelograms with equal diagonals are rectangles.
A quadrilateral with three right angles is a rectangle.
4. Four quadrangles with equal internal angles are rectangles.
5. A parallelogram is a rectangle, and its axisymmetric figure is any set of straight lines connecting the midpoints of opposite sides.
6. For a parallelogram, if the sum of squares of the distances from one point to two pairs of vertices is equal, the parallelogram is a rectangle.
7. A quadrilateral whose diagonal is bisected and equal is a rectangle.
8. A quadrilateral with diagonal lines bisecting each other and internal angles at right angles is a rectangle [edit this paragraph] 1 A quadrilateral with four equilateral sides and four right angles is called a square.
A set of rectangles with equal adjacent sides is a square.
A set of parallelograms with equal adjacent sides and a right angle is a square.
Diamonds with right angles are squares.
A quadrilateral whose diagonal lines are bisected and equal and whose intersection angles are right angles is a square. [Edit this paragraph] 2 Natural edges: two groups of opposite edges are parallel respectively; All four sides are equal; Adjacent sides are perpendicular to each other.
Internal angle: all four angles are 90;
Diagonal lines: Diagonal lines are perpendicular to each other; Diagonal lines are equal and equally divided; Each diagonal bisects a set of diagonal lines;
Symmetry: it is both a central symmetrical figure and an axisymmetric figure (with four axes of symmetry). [Edit this paragraph] 3 Judgment method 1: The rhombus with equal diagonal lines is a square.
2. A rectangle with diagonal lines perpendicular to each other is a square, and a square is a special rectangle.
3: A quadrilateral with four equal sides and three right angles 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 one angle at right angles is a square.
6. A parallelogram with four equal sides and diagonal lines perpendicular to each other is a square.
7. A diamond with a right angle is a square.
The quadrilateral obtained by connecting the midpoints of the sides of the quadrilateral in turn is called the midpoint quadrilateral. No matter how the shape of the original quadrangle changes, the shape of the midpoint quadrangle is always a parallelogram. The midpoint quadrilateral of a square is a square.
8. A quadrilateral whose diagonals are perpendicular, bisected and equal is a square. Trapezoid refers to a set of quadrilaterals whose opposite sides are parallel and the other set of opposite sides are not parallel. Two parallel sides are called the bottom of the trapezoid, and the long side is called the bottom; Non-parallel edges are called waist; The vertical section sandwiched between the two base sides is called the height of the trapezoid. A trapezoid with a waist perpendicular to the bottom is called a right-angled trapezoid, and two trapezoid with equal waist are called isosceles trapezoid. [Edit this paragraph] The properties of isosceles trapezoid 1. The two waists of an isosceles trapezoid are equal.
2. The two bottom angles of the isosceles trapezoid on the same base are equal.
3. The two diagonals of the isosceles trapezoid are equal.
4. The isosceles trapezoid is an axisymmetric figure, and the symmetry axis is a straight line connecting the midpoints of the upper and lower bottom surfaces.
5. The midline of the isosceles trapezoid (the line connecting the midpoints of the two waists is called the midline) is equal to half of the sum of the upper and lower bottoms.
Note: in some cases, the upper and lower bottoms of trapezoid are distinguished by length, not by position. The shorter bottom is called the upper bottom and the longer bottom is called the lower bottom. [Edit this paragraph] Judge 1. A set of quadrangles with parallel opposite sides and another set of quadrangles with non-parallel opposite sides are trapezoid.
2. The isosceles trapezoid is an isosceles trapezoid.
3. A trapezoid with two equal angles on the same base is an isosceles trapezoid.
A trapezoid with right angles is a right trapezoid.
5. A trapezoid with equal diagonal lines is an isosceles trapezoid.