Angles. Projections. Polyhedral angles Angles. Angle between: two intersecting straight lines, two parallel straight lines, two crossing straight lines. Perpendicular to a plane. Projections. Projection of a point and a segment to a plane. Dihedral angle. Linear angle of a dihedral angle. Angle between two planes. Perpendicular planes. Angle between two perpendicular … [Read more...]

## Common notions

Common notions Basic notions of stereometry. Point. Straight line. Plane. Main axiom of stereometry. Pencil of planes. Axis of pencil. Crossing straight lines. Distance between two crossing straight lines. Parallel planes. Parallel straight line and plane. Stereometry studies geometric properties of solid bodies and figures. As well as in planimetry the basic … [Read more...]

## Areas of plane figures

Areas of plane figures Areas of plane figures: square, rectangle, rhombus, parallelogram, trapezoid, quadrangle, right-angled triangle, isosceles triangle, equilateral triangle, arbitrary triangle, polygon, regular hexagon, circle, sector, segment of a circle. Heron's formula. Any triangle. a, b, c – sides; a – a base; h – a height; A, B, C – angles, … [Read more...]

## Inscribed and circumscribed polygons. Regular polygons

Inscribed and circumscribed polygons. Regular polygons Inscribed polygon. Circumscribed polygon. Circumcircle about a polygon. Incircle into a polygon. Radius of an incircle into a triangle. Radius of a circumcircle about a triangle. Regular polygon. Center of a regular polygon. Apothem. Relations between sides and radii of a regular polygon. Inscribed polygon in … [Read more...]

## Geometrical locus. Circle and circumference

Geometrical locus. Circle and circumference Geometrical locus. Midperpendicular. Angle bisector. Circumference. Circle. Arc. Secant. Chord. Diameter. Tangent line. Segment of a circle. Sector of a circle. Angles in a circle. Central angle. Inscribed angle. Circumscribed angle. Radian measure of angles. Round angle. Ratio of circumference length and … [Read more...]

## Similarity of plane figures. Similarity criteria of triangles

Similarity of plane figures. Similarity criteria of triangles Similarity of plane figures. Ratio of similarity. Similarity of polygons. Similarity of triangles. Similarity of right-angled triangles. Similarity of plane figures. If to change ( to increase or to decrease ) all sizes of a plane figure in the same ratio ( ratio of similarity ), then an old and a new … [Read more...]

## Parallelogram and trapezoid

Parallelogram and trapezoid Parallelogram. Properties of a parallelogram. Signs of a parallelogram. Rectangle. Rhombus. Square. Trapezoid. Isosceles trapezoid. Midline of a trapezoid and a triangle. Parallelogram ( ABCD, Fig.32 ) is a quadrangle, opposite sides of which are two-by-two parallel. Any two opposite sides of a parallelogram are called bases, a … [Read more...]

## Triangle

TriangleTriangle. Acute-angled triangle. Right-angled triangle. Obtuse-angled triangle. Isosceles triangle. Equilateral triangle. Scalene triangle. Main properties of triangles. Theorems aboutcongruence of triangles. Remarkable lines and points of a triangle. Pythagorean theorem. Relation of sides for an arbitrary triangle.Triangle is a polygon with three sides (or three … [Read more...]

## Polygon

Polygon Polygon. Vertices, angles, diagonals, sides of a polygon. Perimeter of a polygon. Simple polygons. Convex polygon. Sum of interior angles in a convex polygon. A plane figure, formed by closed chain of segments, is called a polygon. Depending on a quantity of angles a polygon can be a triangle, a quadrangle, a pentagon, a hexagon etc. On Fig.17 the hexagon … [Read more...]

## Euclidean geometry axioms

Euclidean geometry axioms Axiom of belonging. Axiom of ordering. Axiom of congruence (equality) of segments and angles. Axiom of parallel straight lines. Archimedean axiom of continuity. As we have noted above, there is a set of the axioms – properties, that are considered in geometry as main ones and are adopted without a proof . Now, after introducing some … [Read more...]