?
Knowledge points for preparing for the first grade math exam: triangle
I. Definition
1, a figure composed of three line segments that are not on the same line end to end is called a triangle. The angle formed by two adjacent sides is called the inner angle of a triangle, which is called the angle of a triangle for short.
2. a triangle with vertices a, b and c, written as? △ABC？ , read as? Triangle ABC? .
Second, the internal angle of the triangle
1, the sum of the interior angles of the triangle is equal to 180? .
Third, the nature of the triangle external angle
1, one outer angle of a triangle is equal to the sum of two non-adjacent inner angles.
2. The outer angle of a triangle is greater than any inner angle that is not adjacent to it.
3. The sum of the outer angles of the triangle is equal to 360? .
Fourthly, the trilateral relationship of triangle.
1, the sum of any two sides of a triangle is greater than the third side.
2. The triangle is very stable.
Verb (abbreviation for verb) polygon
1. On the plane, a figure composed of some end-to-end line segments is called a polygon.
2. The line segment connecting two nonadjacent vertices of a polygon is called the diagonal of the polygon.
Nitroglycerin. Diagonal formula of n polygon: 2.
Sixth, the sum of the inner angles of a polygon.
1, n The formula of polygon interior angle: (n-2)? 180?
2. The sum of the outer angles of a polygon is equal to 360?
Seven, regular polygon
1. A polygon with equilateral angles is called a regular polygon.
2. The degree of each inner angle of a regular N-polygon is equal to N. ..
?
Knowledge points for preparing for the first grade math exam: axial symmetry
A, axisymmetric graphics
1. Fold along a straight line, and the parts on both sides of the straight line can overlap each other. This figure is called an axisymmetric figure, and this straight line is its axis of symmetry.
2. Axisymmetric figures, such as circles, have more than one axis of symmetry.
Second, axis symmetry.
There is a graph folded along a straight line. If it can overlap with another graphic, Then it is said that these two figures are symmetrical about this line, which is called the symmetry axis, and the overlapping point after folding is the corresponding point, which is called the symmetry point. The symmetry of two graphs about this straight line is also called the symmetry axis.
Thirdly, the nature of graphic symmetry.
What if two graphs are symmetrical? Then the symmetry axis is the median vertical line of the line segment connected by any pair of corresponding points; axis
The symmetry axis of a symmetrical figure is the median vertical line of a line segment connected by any pair of corresponding points.
Fourth, the difference between axisymmetric graphics and axisymmetric graphics
Refers to the shape and position relationship between two figures. Two symmetrical graphs are congruent; Axisymmetric graph is a kind of graph with special shape. An axisymmetric figure is divided into two figures along the axis of symmetry, which are congruent and symmetrical.
Five, the vertical line of the line segment
(1) A straight line passing through the midpoint of a line segment and perpendicular to the line segment. It is called the midline of this line segment (or the midline of the line segment).
(2) The distance between the point on the vertical line in the line segment and the two end points of the line segment is equal; On the other hand, the points that are equidistant from the two endpoints of a line segment are on the midline of this line segment, so the midline of this line segment can be regarded as the set of all points that are equidistant from the two endpoints of this line segment.
6. Make an axisymmetric figure about a straight line.
(1) Do some symmetry points of key points or special points.
(2) Connect the symmetrical points according to the connection mode of the original graph, that is, get the axisymmetric graph of the original graph.
On the Axisymmetry of Coordinates
The coordinates of the point P(x, y) which is axisymmetrical about X are (x, -y).
The coordinates of the point where the point P(x, y) is symmetrical about y are (-x, y).
On the symmetry of the origin
The coordinates of the point where the point P(x, y) is symmetrical about the origin are (-x, -y).
Symmetry of bisector of axis contraction angle
The point P(x, y) is symmetrical about the bisector y=x of the first and third quadrant coordinate axes, and the coordinate of this point is (y, x).
The point P(x, y) is symmetrical about the bisector y= -x of the second and fourth quadrant coordinate axes. The coordinates of this point are (-y, -x) symmetric about the straight line parallel to the coordinate axis.
The coordinate of the point where point P(x, y) is symmetrical about line x=m is (2m-x, y);
The point P(x, y) is symmetrical about the straight line y=n, and the coordinate of this point is (x, 2n-y);
Seven, isosceles triangle
1, definition
A triangle with equal sides is an isosceles triangle. Two equal sides are called waist and the other side is called bottom. The angle between the two sides is called the top angle, and the angle between the waist and the bottom is called the bottom angle.
2. Nature
Attribute 1: The two base angles of an isosceles triangle are equal (abbreviated as? Equal sides and angles? )
Property 2: The bisector, median line and base height of isosceles triangle coincide.
Special: (1) isosceles triangle is an axisymmetric figure.
(2) The midline, angle bisector and height line of the isosceles triangle are equal.
3. Decision theorem
If the two angles of a triangle are equal, then the opposite sides of the two angles are also equal (abbreviated as? Equiangular equilateral? ).
?
Knowledge points of preparing for the first grade mathematics exam: experience uncertainty
I. Decisive events and uncertain events
1. Inevitable events: The events that will happen in each experiment can be determined in advance without experiments.
2. Impossible event: an event that will not happen in every test.
3. Deterministic events: inevitable events and impossible events are collectively referred to as deterministic events.
4. Uncertain event: It is impossible to determine whether it will happen in advance in the experiment.