Lecture
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 planeAngles.
Angle
Types of angles
Angle bisectorTriangle 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 numberThe 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 segmentsSolving triangles.
Cosine theorem
Sine TheoremPolygons.
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 measureSquare 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
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Planometry
Terms: Planometry