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Preliminary geometry

This preliminary mind map of geometric figures summarizes the knowledge of points, lines, surfaces, bodies, straight lines, rays, line segments, angles, geometric figures, etc. Everyone is welcome to learn.

Edited at 2023-07-16 10:09:50

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Preliminary geometry

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Outline

Preliminary geometry

Point, line, surface, body

The intersection of lines is a point, which is the most basic form of geometry.

Lines are divided into straight lines and curves, and are the parts where surfaces intersect.

The body is surrounded by planes and curved surfaces.

Geometry is also called a body.

A point moves to form a line, a line moves to form a surface, and a surface moves to form a body.

Line, ray, line segment

straight line

There are no endpoints, and the straight line represents a straight line AB, which cannot be extended.

Rays

An endpoint, representing ray AB, can be extended in the opposite direction

line segment

Two endpoints, representing line segment a or AB, can be extended or reversely extended.

Two points determine a straight line

Draw a line segment equal to a known line segment

Metrics

Drawing with ruler and compass

How to compare the size of line segments

Metrics

Overlay method

midpoint of line segment

The point that divides a line segment into two equal segments is called the midpoint of the line segment.

If point m is the midpoint of line segment ab, then AM=BM=1/2AB, AB=2AM=2BM

horn

This kind of geometric figure can vividly represent angles. The intersection of the hour hand and the minute hand and the sides of the triangle ruler are all images of angles.

A figure composed of two rays with common endpoints is called an angle

Degrees, minutes and seconds are commonly used units of measurement

Degree: A circumferential angle is divided into 360 equal parts, each part is 1 degree of angle, recorded as 1°

Cent: Divide an angle of 1 degree into 60 equal parts. Each part is called an angle of 1 minute and is recorded as 1'

Second: Divide the angle of 1 minute into 60 equal parts. Each portion is called the angle of 1 second and is recorded as 1''

Angular Comparisons and Operations

Generally starting from the vertex of an angle and dividing it into two equal angles, the ray is called the bisector of the angle.

Supplementary angles and supplementary angles

remaining angle

Two angles whose sum is 90° are supplementary angles, and they are supplementary angles to each other.

Complementary angles of same angles (congruent angles) are equal

supplementary angle

If the sum of two angles is 180°, they are complementary angles.

Supplementary angles of same angles (congruent angles) are equal

Project learning Design and make rectangular-shaped packaging cartons

observe, discuss

design production

communicate, compare

evaluation, summary

consolidate, improve

Geometry

Cuboids, cylinders, spheres, rectangular (square) squares, circles, line segments, points, etc. are all geometric figures. Triangles, quadrilaterals, etc. learned in primary school are also geometric figures. They are all derived from the shapes of various objects.

Some figures are not in the same plane, such as cuboids, cubes, cylinders, cones and spheres, etc. They are called three-dimensional figures.

cylinder

A cylinder is a polyhedron with two parallel and congruent faces, and the intersection lines of the other adjacent faces are parallel. Cylinder and prism are two forms of cylinder.

cone

A cone is a spatial shape defined by a closed plane base and a line segment connecting a point on the base boundary, including cones and pyramids.

Line segments, angles, triangles, rectangles, circles, etc. are all in the same plane, and they are plane figures.

Three-dimensional figures and planar figures are different geometric figures, but they are related. For example, the sides of a cuboid are rectangular.

A three-dimensional figure is surrounded by a planar figure, which can be cut and unfolded into a planar expansion.

Draw n rays arbitrarily inside the angle Then there are (n 1)(n 2)/2 in the graph