Knowledge points of seventh grade mathematics in Shanghai (1)
The case of the root of a linear equation with one variable
△=b2-4ac
When △ > 0, a quadratic equation with one variable has two unequal real roots;
When △=0, the unary quadratic equation has two identical real roots;
When △ < 0, the quadratic equation of one variable has no real root.
Properties of parallelogram:
(1) Two groups of parallelograms with parallel opposite sides are called parallelograms.
(2) The line segment connected by two nonadjacent vertices of a parallelogram is called its diagonal.
③ The opposite sides/diagonals of parallelogram are equal.
(4) The diagonal of the parallelogram is equally divided.
Diamond: ① A group of parallelograms with equal adjacent sides is a diamond.
(2) The four sides of the collar are equal, and the two diagonal lines are equally divided vertically, and each diagonal line is equally divided into a set of diagonal lines.
③ Judgment conditions: define a parallelogram with vertical diagonal and a quadrilateral with equal sides.
Rectangular and square:
(1) There is a right-angled parallelogram called a rectangle.
② The diagonals of a rectangle are equal, and all four corners are right angles.
③ Parallelograms with equal diagonals are rectangles.
④ A square has all the properties of parallelogram, rectangle and diamond.
⑤ A set of rectangles with equal adjacent sides is a square.
Mathematics knowledge points of grade seven in Shanghai (2)
1, there is only one straight line between two points.
2. The line segment between two points is the shortest.
3. The complementary angles of the same angle or equal angle are equal.
4. The complementary angles of the same angle or equal angle are equal.
5. There is one and only one straight line perpendicular to the known straight line.
6. Of all the line segments connecting a point outside the straight line with points on the straight line, the vertical line segment is the shortest.
7. The parallel axiom passes through a point outside the straight line, and there is only one straight line parallel to this straight line.
8. If two straight lines are parallel to the third straight line, the two straight lines are also parallel to each other.
9. The same angle is equal, and two straight lines are parallel.
10, internal dislocation angles are equal, and two straight lines are parallel.
1 1, the inner angles on the same side are complementary, and the two straight lines are parallel.
12, two straight lines are parallel and have the same angle.
13, two straight lines are parallel and the internal dislocation angles are equal.
14. Two straight lines are parallel and complementary.
15, the sum of two sides of a theorem triangle is greater than the third side.
16, the difference between two sides of the inference triangle is smaller than the third side.
17, the sum of the internal angles of the triangle and the theorem triangle is equal to 180?
18, it is inferred that the two acute angles of 1 right triangle are complementary.
19, Inference 2 An outer angle of a triangle is equal to the sum of two inner angles that are not adjacent to it.
20. Inference 3 The outer angle of a triangle is larger than any inner angle that is not adjacent to it.
Knowledge Points of Mathematics in Grade Seven in Shanghai (3)
Parallelogram property theorem 1 parallelogram diagonal equality
Theorem 2 of parallelogram properties: the opposite sides of parallelogram are equal
It is inferred that the parallel segments sandwiched between two parallel lines are equal.
The property theorem of parallelogram The three diagonals of parallelogram are equally divided.
Parallelogram decision theorem 1 Two groups of parallelograms with equal diagonals are parallelograms.
Parallelogram Decision Theorem 2 Two groups of quadrilaterals with equal opposite sides are parallelograms.
Parallelogram Decision Theorem 3 A quadrilateral whose diagonal is bisected is a parallelogram.
Parallelogram Decision Theorem 4 A group of parallelograms with equal opposite sides are parallelograms.
Theorem of Rectangular Properties 1 All four corners of a rectangle are right angles.
Theorem of Rectangular Properties Two diagonal lines of a rectangle are equal.
Rectangular Decision Theorem 1 A quadrilateral with three right angles is a rectangle.
Rectangular Decision Theorem 2 A parallelogram with equal diagonals is a rectangle.
Diamond property theorem 1 All four sides of a diamond are equal.
The property theorem of rhombus Two diagonals of a rhombus are perpendicular to each other, and each diagonal bisects a set of diagonals.
Diamond area = half of diagonal product, that is, S=(a? b)？ 2
Shanghai seventh grade mathematics knowledge related articles;
1. Summary of seventh-grade mathematics knowledge points of Shanghai Education Edition
2. The seventh grade mathematics knowledge summary
3. The seventh grade mathematics knowledge points induction
4. Summary of mathematical knowledge points in the first volume of the seventh grade
5. Summary of knowledge points in the first volume of seventh grade mathematics