Mandatory theoretical part, the knowledge of which is necessary to receive a credit in geometry in the 1st quarter of grade 7.
The only and strict requirement is verbatim memorization of the entire volume of theoretical material.
Only one line can be drawn through two points .
Two lines can only have one common point .
A segment is a part of a straight line bounded on both sides by points .
A ray is a straight line, bounded at one end and unbounded at the other.
An angle is a geometric figure formed by two rays emanating from one point ( corner vertex).
The angle is indicated by the symbol and three letters denoting the ends of the rays and the top of the corner, for example, AOB (moreover, the letter of the top is the middle one).
A straight angle is an angle where both sides lie on the same straight line. The measure of a straight angle is 180 degrees.
Adjacent angles are angles that have a common vertex and a common side, and the other two sides are continuations of one another.
AOB and COB related
The sum of adjacent angles is 180°.
Vertical angles are two angles with a common vertex, in which the sides of one are extensions of the sides of the other.
AOB and COD (as well as AOC and DOB) – vertical angles.
Vertical angles are equal.
The bisector of an angle is a ray that bisects the angle.
Angle bisector property: Each point of an angle’s bisector is the same distance from the sides of that angle .
Bisectors of adjacent angles are mutually perpendicular.
Bisectors of vertical angles are continuations of one another.
Figures are said to be equal if they match when superimposed .
Intersecting lines forming a right angle are called mutually perpendicular.
If the lines AB and MK are perpendicular, then this is denoted: AB MK.
From a point not lying on a line, one can draw a perpendicular to this line, and only one.
A triangle is a geometric figure consisting of three points that do not lie on the same straight line, connected by segments.
A triangle is called isosceles if two of its sides are equal.
Equal triangles have equal angles opposite equal sides.
The median of a triangle is the line segment that connects the vertex of the triangle to the midpoint of the opposite side.
The height of a triangle is the perpendicular drawn from the vertex of the triangle to the line containing the opposite side.
The bisector of a triangle is a segment of the bisector of the angle of a triangle that connects the vertex of the triangle to a point on the opposite side.
The first sign of equality of triangles.
If two sides and the angle between them of one triangle are respectively equal to two sides and the angle between them of another triangle, then such triangles are congruent.
A proof is an argument that establishes a property.
A theorem is a statement that establishes some property and requires proof. Theorems are also called lemmas, properties, corollaries, rules, signs, statements. In proving the theorem, we rely on previously established properties; some of them are also theorems.
An axiom is a statement that establishes some property and is accepted without proof.