Property: Two straight lines intersect with only one intersection point.

Second, the vertex angle, adjacent complementary angle:

1. Diagonal: As shown in the figure, straight lines AB and CD intersect at point O, while ∠ 1 and ∠2 have a common vertex O, and their two sides are opposite extension lines, so these two angles are called diagonal.

Note: Two angles must satisfy two conditions of vertex angle: (1) has a common vertex; (2) The two sides are opposite extension lines.

2. Adjacent complementary angles: As shown in the figure, ∠ 1 and ∠2 have a common edge OC, and their other edges OA and OB are opposite extension lines, which are obviously complementary. Two angles with this relationship are called complementary angles that are adjacent to each other.

3. Attribute: (1) equals the vertex angle; (2) The sum of two adjacent complementary angles is equal to.

3. The concept and properties of vertical line: 1. Concept: If one of the four angles formed by the intersection of two straight lines is a right angle, the two straight lines are said to be perpendicular to each other, one of which is called the perpendicular of the other straight line, and their intersection is called the vertical foot.

Note: verticality is a special case of intersection.

2. Distance from point to straight line: The length from a point outside the straight line to the vertical section of this straight line is called the distance from point to straight line.

Note: Vertical lines are straight lines and vertical line segments are line segments. The distance from the point to the straight line does not refer to the vertical line segment, but refers to the length of the vertical line segment.

3. Distance between parallel lines: The length of a line segment perpendicular to and sandwiched between two parallel lines is called the distance between two parallel lines. The distance between parallel lines is equal everywhere.

4. Properties: (1) The four angles formed by the intersection of two perpendicular lines are right angles; (2) Draw a vertical line of a known straight line through a point on the straight line or a point outside the straight line, and only one vertical line can be drawn; (3) Of all the line segments connecting a point outside the straight line and a point on the straight line, the vertical line segment is the shortest. To put it simply: the vertical segment is the shortest; (4) The distance between parallel lines is equal everywhere.

Four. Equilibrium angle, internal dislocation angle and ipsilateral internal angle:

As shown in the figure, straight lines AB and CD are cut into eight angles by the third straight line EF, which is called "three-line octagon" for short.

1. Isomorphism angles: ∠ 1 and ∠5, ∠2 and ∠6, ∠3 and ∠7, ∠4 and ∠8, which are on the same side of AB and CD respectively, and in EF. The conformal angle is F-shaped;

2. Internal dislocation angles: ∠ 3 and ∠ 5, ∠ 4 and ∠ 6, which are respectively sandwiched between AB and CD and on both sides of EF. The internal dislocation angle is z-shaped;

3. The internal angles of the same side: ∠ 4 and ∠ 5, ∠ 3 and ∠ 6, which are respectively sandwiched between AB and CD and on the same side of EF. The inner angle of the same side is U-shaped.

Description: (1) equilibrium angle, internal dislocation angle and ipsilateral internal angle refer to two angles with special positional relationship;

(2) These three types of angles are all formed by cutting two straight lines by a third straight line;

(3) Balanced angle characteristics: the cutting lines are on the same side and the cutting lines are in the same direction; Internal dislocation angle characteristics: on both sides of the cutting line, between two cutting line segments; The characteristics of the inner angle on the same side: the cutting lines are on the same side and cut between two line segments;

(4) Among the eight angles cut by the third line, there are 4 pairs of congruent angles, 2 pairs of internal dislocation angles and 2 pairs of internal angles on the same side.