A method that proves that two straight lines are parallel, a method that proves that two straight li

1.Definition of parallel lines (In the same plane, two straight lines that do not intersect are called parallel lines. ）2.Axiom of parallelism follows that two straight lines parallel to the same line are parallel to each other.

3.In the same plane, two straight lines perpendicular to the same line are parallel to each other.

4.The isotope angles are equal, and the two straight lines are parallel.

5.The inner staggered angles are equal, and the two straight lines are parallel.

6.The inner angles of the same side are complementary, and the two straight lines are parallel.

In the same plane, passing a point outside the straight line, there is one and only one straight line parallel to the straight line.

Corollary of the axiom of parallelism: (Parallel transitivity) If both lines are parallel to the third line, then the two lines are also parallel to each other.

That is, two straight lines parallel to the same straight line are parallel.

The isotope angle is equal, the internal misalignment angle is equal, and the lateral internal angle is complementary.

It is enough to prove that the distance between any two points of two straight lines on the same plane is equal, and you can put the problem on it and I will show it for you.

The isotope angle is equal, the same side inner angle is complementary, and the internal wrong angle is equal, and the above three points can be.

You can first prove that it is a parallelogram.

1.Lines perpendicular to the same line are parallel.

2.Two straight lines with equal isotopic angles, equal internal wrong angles, or complementary internal angles to the same side are parallel.

3.The opposite sides of the parallelogram are parallel.

4.The median line of the triangle is parallel to the third side.

5.The median line of the trapezoid is parallel to the two bases.

6.Two lines parallel to the same line are parallel.

7.A straight line cuts the two sides (or extensions) of the triangle and results in a line segment that is proportional to each other, and the line is parallel to the third side.

Prove that two straight lines are perpendicular to each other.

1.The apex bisector of an isosceles triangle or the midline at the bottom is vertically haired.

2.If the middle line of one side of a triangle is equal to half of this side, then the angle opposite that side is a right angle.

3.In a triangle, if two corners are left to the other, the third angle is a right angle.

4.The bisector of the adjacent complementary angles is perpendicular to each other.

5.If a straight line is perpendicular to one of the parallel lines, it must be perpendicular to the other.

6.When two straight lines intersect at right angles, the two straight lines are perpendicular.

8.The inverse theorem that makes use of the Pythagorean theorem.

9.The diagonal lines of the diamond are perpendicular to each other.

10.In a circle, the diameter of the bisector chord (or arc) is perpendicular to the chord.

11.The circumferential angle on the utilized semicircle is a right angle.

Prove that two straight lines are parallel to a simple judgment method:

1) Isotope angle.

Equal, two straight lines are parallel.

2) Wrong angles.

Equal, two straight lines are parallel.

3) Same as the inner corner.

Complementary, two straight lines parallel.

4) In the same plane, two straight lines do not intersect, that is, parallel and coincide.

5) If two straight lines are parallel to one straight line, then the three non-overlapping straight lines are parallel to each other.

The nature of two straight lines parallel to each other:

1) Two straight lines are parallel and the isotope angles are equal.

2) The two straight lines are parallel, and the inner wrong angles are equal.

3) The two straight lines are parallel and complementary to the side inner angles.

4) If both lines are parallel to the third line, then the two lines are also parallel to each other.

1.According to the Pythagorean theorem of a right triangle, if two straight lines are parallel, the two right angles formed after intersection are 90 degrees;

2.It can be proved by the vector method that if two straight lines are parallel, then the two normal vector modulus are equal in length and perpendicular to each other.

3.It is proved by the proportional method that if two straight lines are parallel, their slopes are equal;

4.It is proved by the parametric equation that if two straight lines are parallel, the slope of the straight line of the parametric equation is equal.

Let the two linear equations be.

ax+by+c1=0

ax+by+c2=0

The distance between two parallel straight lines is the distance from any point on a straight line to another straight line, let the point p(a,b) on the straight line ax+by+c1=0, then satisfy aa+bb+c1=0, that is, ab+bb=-c1, from the point to the straight line distance formula, p to the straight line ax+by+c2=0 distance is.

d=|aa+bb+c2|/√a^2+b^2)=|c1+c2|/√a^2+b^2)

c1-c2|/√a^2+b^2)

If it helps you, please remember, o( o thank you.

In the same plane, two straight lines that do not intersect are called parallel lines. Determination method of parallel lines: two straight lines parallel to the same straight line are parallel to each other; In the same plane, two straight lines perpendicular to the same line are parallel to each other. The isotope angles are equal, and the two straight lines are parallel.

Triangle classification1. Unequal triangle: An unequal triangle refers to a triangle with three unequal sides.

2. Isosceles triangle: Isosceles triangle refers to a triangle with equal sides, and the two equal sides are called the waist of this triangle. In an isosceles triangle, the two equal sides are called the waist of the triangle, and the other side is called the bottom side.

The angle between the two waists is called the top angle, and the angle between the waist and the bottom is called the bottom angle. The two bases of an isosceles triangle have equal numbers of angles (abbreviated as "equilateral to equal angles"). The bisector of the apex of the isosceles triangle, the middle line on the base, and the high overlap on the base (abbreviated as "the three-in-one nature of the grinding rock isosceles triangle").

3. Equilateral triangles. An equilateral triangle (also known as a regular triangle) is a triangle with three equal sides, and its three internal angles are equal, all of which are 60°, and it is a type of acute triangle. Equilateral triangles are also the most stable structure.

Equilateral triangles are special isosceles triangles, so equilateral triangles have all the properties of isosceles triangles.