Mathematics of Grade Two, Book One, Geometry Knowledge One
1, triangle: A figure composed of three line segments that are not on the same line 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 its relative midpoint 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 angle between one side of the triangle and the extension line of the other side is called the external angle of the triangle.
1 1, the properties of the external 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? .
Mathematics of Grade Two, Book One, Geometry Knowledge II
Summary of knowledge points and concepts of quadrilateral (including polygon)
First, the definition, nature and judgment of parallelogram
1, two groups of parallelograms with opposite sides 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.
Mathematics of Grade Two, Book One, Geometry Knowledge III
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 trapezoid. 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 midline 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.
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