Determination content:
(1) Two groups of parallelograms whose opposite sides are parallel and equal are parallelograms.
parallelogram
(2) The quadrilateral bisected by two diagonal lines is a parallelogram;
(3) Two groups of quadrangles with equal diagonal are parallelograms.
Main attributes
Rectangular, rhombic and square are all special parallelograms. )
nature
(1) If a quadrilateral is a parallelogram, then two opposite sides of the quadrilateral are equal.
(Simply stated as "two opposite sides of a parallelogram are equal")
(2) If the quadrilateral is a parallelogram, then the two diagonal corners of the quadrilateral are equal.
(Simply stated as "the two diagonals of a parallelogram are equal respectively")
(3) If a quadrilateral is a parallelogram, then the adjacent angles of this quadrilateral are complementary.
(simply described as "complementary adjacent angles of parallelogram")
(4) The parallel segments sandwiched between two parallel lines are equal.
(5) If a quadrilateral is a parallelogram, then the two diagonals of this quadrilateral are equally divided.
(short for "the diagonal of a parallelogram is divided equally")
(6) The figure obtained by connecting the midpoints of any quadrilateral side is a parallelogram. (inference)
(7) The area of a parallelogram is equal to the product of the base and the height. (It can be considered as a rectangle)
(8) The line crossing the diagonal intersection of the parallelogram divides the parallelogram into two congruent parts.
(9) A parallelogram is a central symmetric figure, and the center of symmetry is the intersection of two diagonals.
(10) The parallelogram is not axisymmetrical, but the rectangle and the diamond are axisymmetrical. Note: Square, rectangle and diamond are also special parallelograms, and they have the properties of parallelograms.
Parallelogram (1 1) In the parallelogram ABCD (as shown in the figure), if E is the midpoint of AB, then AC and DE are equally divided. Generally speaking, if E is the bisector of N near A on AB, then AC and DE are bisectors (n+ 1).
(12) In the parallelogram ABCD, if AC and BD are diagonals of the parallelogram ABCD, the sum of squares of the four sides is equal to the sum of squares of the diagonals.
(13) The diagonal of the parallelogram divides the area of the parallelogram into four equal parts.
(14) In a parallelogram, the included angle formed by the heights of two different opposite sides, the smaller angle is equal to the smaller angle in the parallelogram, and the larger angle is equal to the larger angle in the parallelogram.
(15) In a parallelogram, the height formed by the vertex of an angle and its diagonal sides is equal to the included angle formed by the two sides of the angle.
Area formula
parallelogram
The area formula of (1) parallelogram: base× height (the derivation method is shown in the figure); If "h" is used for height, "a" for base and "s" for parallelogram area, then s is parallel to four sides =ah.
(2) The area of the parallelogram is equal to the product of two adjacent sides multiplied by the sine value of the included angle; If "A" and "B" represent the lengths of two groups of adjacent sides, S represents the sine value of the included angle between the two sides, and "S" represents the area of the parallelogram, then S parallelogram = A "B * S.
Perimeter formula
The perimeter of the parallelogram can be squared (radix 1+ radix 2); If "a" represents the base 1, "b" represents the base 2, and "c-plane" represents the perimeter of a parallelogram, then the perimeter of four parallel sides is c=2*(a+b), and the base × 1X is high.
Formula description
If "h" is used for height, "a" for base and "s" for parallelogram area, then s is parallel to four sides =ah.
Main categories
1, parallelogram is a plane figure.
2. Parallelogram belongs to quadrilateral.
3. Parallelogram also includes special parallelograms: rectangle, square and diamond.
4. Parallelogram is a figure with central symmetry.
Special parallelogram
1, parallelogram+right angle = rectangle
2, parallelogram+a group of adjacent sides equal = diamond.
3, parallelogram+right angle+a group of adjacent sides equal = square
rectangle
1. Definition: A parallelogram with a right angle is called a rectangle.
2. Attribute: (1) All four corners of the rectangle are right angles.
(2) The diagonals of the rectangles are equal.
(3) It has the property of parallelogram.
3. Judgment: (1) A parallelogram with right angles is a rectangle (definition).
(2) Parallelograms with equal diagonals are rectangles.
(3) A quadrilateral with three right angles is a rectangle.
diamond
1. Definition: A set of parallelograms with equal adjacent sides is called a diamond.
2. Property: (1) All four sides of the diamond are equal.
(2) The diagonal lines of the diamond are perpendicular to each other, and each diagonal line bisects a set of diagonal lines.
(3) It has the property of parallelogram.
3. Judgment: (1) A set of parallelograms with equal adjacent sides is a diamond (definition).
(2) Parallelograms with diagonal lines perpendicular to each other are rhombic.
(3) A quadrilateral with four equilateral sides is a diamond.
(4) The quadrilateral bisecting the diagonal vertically is a diamond.
square
1. Definition: A set of parallelograms with equal adjacent sides and a right angle is a square.
2. Properties: both rectangular and rhombic.
3. Judgment: 1: The rhombus with equal diagonals is a square. 2. Diamonds with right angles are squares.
3: Rectangles with diagonal lines perpendicular to each other are squares. 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 vertical and equal diagonals is a square.
7: A quadrilateral whose diagonals are perpendicular, bisected and equal is a square.
8: A set of quadrilaterals with equal adjacent sides and three right angles is a square.
∠EMC+∠DMC = 100+50 = 150