What are the knowledge points of mathematical geometry in the second day of junior high school?

Mathematical geometry problem is a big death point for students. If you want to learn math and geometry well in senior two, you need to find a correct learning method. In order to help you learn Math Geometry in Senior Two better, here are the knowledge points I shared with you. I hope you like it!

Knowledge point one of mathematics and geometry in the second day of junior high school

Summary of knowledge points and concepts of quadrilateral (including polygon)

First, the definition, nature and judgment of parallelogram

1. Two groups of parallelograms are parallelograms.

2. Nature:

(1) The opposite sides of the parallelogram are equal and parallel.

(2) The diagonals of the parallelogram are equal and the adjacent angles are complementary.

(3) The diagonal of the parallelogram is equally divided.

3. Judges:

(1) Two groups of parallelograms with parallel opposite sides are parallelograms.

(2) Two groups of quadrangles with equal opposite sides are parallelograms.

(3) A set of quadrilaterals with parallel and equal opposite sides is a parallelogram.

(4) Two groups of quadrangles with equal diagonal are parallelograms.

(5) The quadrilateral whose diagonals bisect each other is a parallelogram.

4. Symmetry: A parallelogram is a figure with central symmetry.

Second, the definition, nature and judgment of rectangle

1. Definition: A parallelogram with a right angle is called a rectangle.

2. Properties: The four corners of a rectangle are right angles, and the diagonals of the rectangle are equal.

3. Judges:

A parallelogram with a right angle is called a rectangle.

(2) A quadrilateral with three right angles is a rectangle.

(3) Two parallelograms with equal diagonals are rectangles.

4. Symmetry: the rectangle is an axisymmetric figure and a central symmetric figure.

Third, the definition, nature and judgment of diamonds.

1. Definition: A set of parallelograms with equal adjacent sides is called a diamond.

(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) The diamond is divided into four congruent right triangles by two diagonal lines.

(4) The area of the diamond is equal to half of the product of two diagonals.

2.s diamond = 6(n and 6 are diagonal lengths respectively)

3. Judges:

(1) A group of parallelograms with equal adjacent sides is called a diamond.

(2) A quadrilateral with four equilateral sides is a diamond.

(3) Parallelograms with diagonal lines perpendicular to each other are rhombic.

4. Symmetry: Diamonds are axisymmetrical and centrosymmetric.

Four. Definition, Properties and Judgment of Square

1. Definition: A group of parallelograms with equal adjacent sides and a right angle is called a square.

2. Nature:

(1) All four corners of a square are right angles and all four sides are equal.

(2) The two diagonals of a square are equal and vertically bisected, and each diagonal bisects a set of diagonals.

(3) A diagonal line of the square divides the square into two isosceles right triangles.

(4) The included angle between the diagonal and the side of a square is 45?

(5) The two diagonals of the square divide the square into four congruent isosceles right triangles.

3. Judges:

(1) First determine that a quadrilateral is a rectangle, and then determine that a group of adjacent sides are equal.

(2) First, judge that a quadrilateral is a diamond, and then judge that an angle is a right angle.

4. Symmetry: A square is an axisymmetric figure and a centrally symmetric figure.

The definition of verb (abbreviation of verb) trapezoid, the nature and judgment of isosceles trapezoid

1. Definition: A set of quadrangles with parallel opposite sides and another set of quadrangles with non-parallel opposite sides are trapezoid. An isosceles trapezoid is an isosceles ladder.

A trapezoid with a waist perpendicular to the bottom is a right-angled trapezoid.

2. The nature of isosceles trapezoid: the two waists of isosceles trapezoid are equal; Two angles on the same base are equal; The two diagonals are equal.

3. Determination of isosceles trapezoid: isosceles trapezoid is isosceles trapezoid; Two trapezoid with equal angles on the same base are isosceles trapezoid; Two trapeziums with equal diagonals are isosceles trapeziums.

4. Symmetry: The isosceles trapezoid is an axisymmetric figure.

6. The midline of the triangle is parallel to the third side of the triangle and equal to half of the third side; The center line of the trapezoid is parallel to the two bottom sides of the trapezoid and equal to half of the sum of the two bottom sides.

Seven, the center of gravity of the line segment is the midpoint of the line segment; The center of gravity of parallelogram is the intersection of two diagonal lines; The center of gravity of a triangle is the intersection of three midlines.

Eight, the quadrilateral obtained by connecting the midpoints of the sides of any quadrilateral in turn is called the midpoint quadrilateral.

Nine, polygon

1. Polygon: On the plane, a figure consisting of some line segments connected end to end is called a polygon.

2. Interior angle of polygon: The angle formed by two adjacent sides of polygon is called its interior angle.

3. Exterior angle of polygon: the angle formed by the extension line of one side of polygon and its adjacent side is called the exterior angle of polygon.

4. Diagonal polygon: The line segment connecting two nonadjacent vertices of a polygon is called diagonal polygon.

5. Classification of polygons: it can be divided into convex polygons and concave polygons. Convex polygons can also be called plane polygons and concave polygons can also be called space polygons. Polygons can also be divided into regular polygons and non-regular polygons. Regular polygons have equal sides and equal internal angles.

6. Regular polygon: A polygon with equal angles and sides in a plane is called a regular polygon.

7. Plane mosaic: covering a part of a plane with some non-overlapping polygons is called covering the plane with polygons.

8. Formulas and attributes

Formula for the sum of polygon internal angles: Is the sum of n polygon internal angles equal to (n-2)? 180?

9. The theorem of polygon exterior angle sum;

(1) Is the sum of the outer angles of the n-polygon equal to n? 180? -(n-2)？ 180? =360?

(2) Every inner angle of a polygon and its adjacent outer angles are adjacent complementary angles, so the sum of the inner and outer angles of n polygons is equal to n? 180?

10. Number of diagonal lines of polygon:

(1) Starting from a vertex of an n polygon, (n-3) diagonal lines can be drawn, and the polygon can be divided into (n-2) triangles.

(2) An n-side * * has n(n-3)/2 diagonals.

Knowledge points of mathematics and geometry in the second day of junior high school

Recycle knowledge points and concept summary

1. Three points that are not on the same straight line determine a circle.

2. Vertical diameter theorem: the diameter perpendicular to the chord bisects the chord and bisects the two arcs opposite the chord.

Inference 1 ① (not diameter) has a diameter perpendicular to the chord and bisects the two arcs opposite to the chord.

(2) The perpendicular line of the chord passes through the center of the circle and bisects the two arcs opposite to the chord.

③ bisect the diameter of an arc opposite to the chord, bisect the chord vertically, and bisect another arc opposite to the chord.

Inference 2 The arcs between two parallel chords of a circle are equal.

3. A circle is a central symmetrical figure with the center of the circle as the symmetrical center.

4. A circle is a set of points whose distance from a fixed point is equal to a fixed length.

5. The interior of a circle can be regarded as a collection of points whose center distance is less than the radius.

6. The outside of a circle can be regarded as a collection of points whose center is farther than the radius.

7. The same circle or the same circle has the same radius.

8. The distance to a fixed point is equal to the trajectory of a fixed-length point, which is a circle with the fixed point as the center and the fixed length as the radius.

9. Theorem In the same circle or in the same circle, the isocentric angle has equal arc, chord and chord center distance.

10. It is inferred that in the same circle or equal circle, if one set of quantities in two central angles, two arcs, two chords or the chord-center distance between two chords is equal, the corresponding other set of quantities is also equal.

1 1. Theorem: Diagonal lines of inscribed quadrangles of a circle are complementary, and any external angle is equal to its internal angle.

12.① intersection point d of straight line l and ⊙O

(2) the tangent of the straight line l, and ⊙ o d = r.

③ Lines L and ⊙O are separated from each other d>r.

13. Judgment theorem of tangent: The straight line passing through the outer end of the radius and perpendicular to the radius is the tangent of the circle.

14. Tangent theorem: the tangent of a circle is perpendicular to the radius passing through the tangent point.

15. Inference 1 A straight line passing through the center of the circle and perpendicular to the tangent must pass through the tangent point.

16. Inference 2 A straight line that crosses the tangent point and is perpendicular to the tangent must pass through the center of the circle.

17. Tangent length theorem: two tangents drawn from a point outside the circle are equal in length, and the connecting line between the center of the circle and this point bisects the included angle of the two tangents.

18. The sum of two opposite sides of the circumscribed quadrangle of a circle is equal, and the outer angle is equal to the inner diagonal.

19. If two circles are tangent, then the tangent point must be on the line.

20.① Two circles are separated by d>. R+r

(2) circumscribed circle d d = r+r.

(3) the intersection of two circles R-rr)

④ inscribed circle d = r-r (r >); R) (5) Two circles contain dr)

2 1. Theorem: The intersection line of two circles bisects the common chord of two circles vertically.

22. Theorem: Divide a circle into n(n? 3):

(1) The polygon obtained by connecting the points in turn is the inscribed regular N-polygon of this circle.

(2) A polygon whose vertex is the intersection of adjacent tangents is a circumscribed regular N polygon of a circle.

Theorem: Any regular polygon has a circumscribed circle and an inscribed circle, which are concentric circles.

24. Every inner angle of a regular N-polygon is equal to (n-2)? 180? /n

25. Theorem: The radius and vertex of a regular N-polygon divide the regular N-polygon into 2n congruent right triangles.

26. The area of a regular N-polygon Sn=pnrn/2 p represents the perimeter of the regular N-polygon.

27. regular triangle area? 3a/4 a indicates the side length.

28. If there are K positive N corners around a vertex, the sum of these angles should be 360? , so k? (n-2) 180？ /n=360？ It becomes (n-2)(k-2)=4.

29. Calculation formula of arc length: L = nσR/ 180.

30. Sector area formula: s sector =n r 2/360 = LR/2.

3 1. Inner common tangent length = d-(R-r) Outer common tangent length = d-(R+r)

32. Theorem: The angle of the circle subtended by an arc is equal to half of the central angle subtended by it.

33. Inference 1 is equal to the circumferential angle of the same arc or equal arc; In the same circle or in the same circle, the arcs of equal circumferential angles are also equal.

34. Inference 2 The circumference angle (or diameter) of a semicircle is a right angle; 90? The chord opposite to the circumferential angle is the diameter.

35. the arc length formula l=a*r a is the radian number of the central angle r >; 0 sector area formula s= 1/2*l*r

The third knowledge point of mathematical geometry in the second day of junior high school

Summary of triangle knowledge points and concepts

1. triangle: A figure composed of three line segments that are not on the same line and are connected end to end is called a triangle.

2. Classification of triangles

3. Trilateral relationship of triangle: the sum of any two sides of triangle is greater than the third side, and the difference between any two sides is less than the third side.

4. Height: Draw a vertical line from the vertex of the triangle to the line where the opposite side is located, and the line segment between the vertex and the vertical foot is called the height of the triangle.

5. midline: in a triangle, the line segment connecting the vertex and the midpoint of its opposite side is called the midline of the triangle.

6. Angular bisector: The bisector of the inner angle of a triangle intersects the opposite side of this angle, and the line segment between the intersection of the vertex and this angle is called the angular bisector of the triangle.

7. Significance and practice of high line, middle line and angle bisector.

8. Stability of triangle: The shape of triangle is fixed, and this property of triangle is called stability of triangle.

9. Theorem of the sum of triangle internal angles: The sum of the three internal angles of a triangle is equal to 180?

It is inferred that the two acute angles of 1 right triangle are complementary.

Inference 2 An outer angle of a triangle is equal to the sum of two non-adjacent inner angles.

Inference 3: One outer angle of a triangle is larger than any inner angle that is not adjacent to it; The sum of the inner angles of a triangle is half of the sum of the outer angles.

10. External angle of triangle: the included angle between one side of triangle and the extension line of the other side is called the external angle of triangle.

1 1. The Properties of the Exterior Angle of Triangle

(1) Vertex is the vertex of a triangle, one side is one side of the triangle, and the other side is the extension line of one side of the triangle;

(2) An outer angle of a triangle is equal to the sum of two inner angles that are not adjacent to it;

(3) The outer angle of a triangle is greater than any inner angle that is not adjacent to it;

(4) The sum of the external angles of a triangle is 360? .

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