Planimetry

Planimetry.

Basic concepts. Properties of the simplest geometric shapes.

Straight and point

Section

Semi-straight beam

Perpendicular straight lines

Parallel straight lines. The angles that occur when crossing.

A sign of parallel lines.

Half plane

Angles.

Angle

Types of angles

Angle bisector

Triangle and its properties.

Triangle

Types of triangles

Equality of triangles

The height, median and bisector of the triangle

The first sign of equality of triangles

A sign of parallel lines

The second sign of equality of triangles

Parallel straight lines. Properties

Equilateral triangle.

Properties of angles of an isosceles triangle.

Sign of an isosceles triangle.

The median property of an isosceles triangle.

The property of the median and height of an isosceles triangle.

The third sign of equality of triangles.

The sum of the corners of the triangle.

The sum of the corners of the triangle.

The outer corners of the triangle.

Right triangle.

The existence and uniqueness of the perpendicular to the line.

The distance from the point to the line.

Geometric constructions.

Circle.

Touch the circles.

Circle properties

The circumference described near the triangle.

Middle perpendicular. Mediatrix.

Circle inscribed in a triangle.

Building shapes.

Construction of a triangle with given sides.

Construction of an angle equal to this.

Construction of the bisector of the angle.

Dividing the segment in half.

Construction of a perpendicular line.

Construction of the fourth proportional segment.

Quadrangles.

Quadrangle.

Parallelogram. Signs of parallelogram.

Properties of the parallelogram.

Rectangle. Sign of the rectangle.

Rectangle properties.

Rhombus. Signs of rhombus.

Diamond property.

Square. Sign of the square.

Thales theorem.

The middle line of the triangle.

Trapeze.

Trapezoid properties.

The theorem on proportional segments.

Pythagorean theorem.

Cosine of the angle.

Pythagorean theorem.

Triangle inequality.

Sine and tangent angle.

Cartesian coordinates on the plane.

Cartesian coordinates on the plane.

The distance between the points.

The middle of the segment.

The equation of a circle.

Equation of a line.

The coordinates of the point of intersection of the lines.

The position of the line relative to the coordinate system.

The angular coefficient in the equation is straight. The geometric meaning of the coefficient.

Motion.

Transform shapes.

Properties of motion.

Symmetry about a point.

The symmetry property with respect to a point.

Symmetry is relatively straightforward.

The symmetry property is relatively straight.

Turn.

Parallel carry.

The parallel transfer property.

Co-directional semi-direct.

Similarity conversion.

Vector.

Vector.

Single vector.

Collinear vector.

Collinear vector. Properties

Coordinates of the vector.

Coordinates of the vector. Properties

Equality of vectors.

Scalar product.

Scalar product. Property.

Addition of vectors.

Addition of vectors. Parallelogram rule

Addition of vectors. Triangle rule

Addition of vectors. Difference

The property of multiplying a vector by a number

Multiply vector by number

The similarity of figures.

Homotetia.

Homotetia. Property

Similarity of figures

Sign of the similarity of triangles at two angles

Sign of similarity of triangles on two sides and angles between them

Sign of similarity of triangles on three sides

Corners inscribed in a circle

Angles inscribed in a circle. Property

Proportionality of chord segments

Solving triangles.

Cosine theorem

Sine Theorem

Polygons.

Broken

Convex polygons

Convex polygons. Property

Regular polygons

Formula for the radii of inscribed circles of regular polygons

The formula for the radii of the circumscribed circles of regular polygons

Circumference

Radian angle measure

Square figures.

Square

Rectangle area

Parallelogram area

Area of ​​a triangle

Trapezium area

Circle, circular segment, circular sector

Area of ​​a circle

Area of ​​a circular sector

Circular segment area