"Positional Relationship of Two Straight Lines" Parallel Lines and Intersecting Lines PPT Courseware

Description

"Positional Relationship of Two Straight Lines" Parallel Lines and Intersecting Lines PPT Courseware

Return to textbooks

1. If two straight lines have one and only one common point, then the two straight lines intersect; if there is no common point, then the two straight lines are parallel; if there are countless common points, then the two straight lines coincide.

Linear system equations

(1) The equation of the straight line passing through the intersection of two straight lines l1 and l2 is set to A1x+B1y+C1+λ(A2x+B2y+C2)=0 (excluding l2);

(2) The equation of the straight line parallel to Ax+By+C=0 is set to Ax+By+m=0 (m≠C);

(3) The equation of the straight line perpendicular to Ax+By+C=0 is set to Bx-Ay+n=0;

(4) The equation of the straight line passing through the fixed point (x0, y0) is set to y-y0=k(x-x0) and x=x0.

Test center sparring partner

1. (2011·Shaanxi Eighth School Simulation) It is known that two straight lines l1: ax+by+c=0, l2: mx+ny+p=0, then an=bm is the () of the straight line l1∥l2

A. Sufficient and unnecessary conditions B. Necessary and insufficient conditions

C. Necessary and sufficient conditions D. Neither sufficient nor necessary conditions

Analysis: ∵l1∥l2⇒an-bm=0, and an-bm=0⇒/l1∥l2, so an=bm is a necessary and insufficient condition for the straight line l1∥l2.

Answer: B

3． If point P(3,4) and point Q(a,b) are symmetrical about the straight line x-y-1=0, then ()

A. a=1, b=2 B． a=2, b=-1

C. a=4, b=3 D． a=5, b=2

4. If A(-4,2), B(6,-4), C(12,6), D(2,12), then the correct number of the following four conclusions is ()

①AB∥CD; ②AB⊥AD; ③|AC|＝|BD|; ④AC⊥BD

A. 1B. 2

C. 3D. 4

Type 1: Parallel and perpendicular of two straight lines

Problem-solving preparation: For two straight lines that do not overlap, when the slopes of both straight lines do not exist, the two straight lines are parallel; when the slope of one straight line does not exist and the slope of the other straight line is 0, the two straight lines are perpendicular; when the slope of one straight line does not exist, the two straight lines are perpendicular. If the slope does not exist and the slope of the other straight line is a non-zero real number, then the two straight lines intersect but are not perpendicular.

[Typical example 1] Given that straight line l1: mx+8y+n=0 and straight line l2: 2x+my-1=0, find the values ​​of real numbers m and n according to the following situations respectively.

(1) l1 and l2 are parallel;

(2) l1 and l2 are perpendicular.

Type 2: Intersection, angle and included angle problems of two straight lines

Problem-solving preparation: When applying knowledge of plane geometry to find the straight lines where each side of a geometric figure lies, the included angle and arrival angle formulas are often used. Pay attention to collecting the information contained in the known conditions in order to select the formula. Do not blindly use the two formulas without considering the characteristics of the figure. practice. If you are not sure which straight line is the angle to which straight line, you can first use the angle formula to calculate and then use graphics or other conditions of the question to check and make choices on the calculation results.

Exploration 1: As shown in the figure, it is known that the three-sided equations of △ABC are AB: 4x-3y+10=0, BC: y-2=0, CA: 3x-4y-5=0, find:

(1) The size of ∠B;

(2) The equation of the straight line where the angle bisector of ∠BAC lies;

(3)The high point on the edge of AB

Exploration 2: Given point P(2,-1), find:

(1) The equation of the straight line l passing through point P and the distance from the origin is 2;

(2) What is the equation of the straight line l that passes through point P and has the largest distance from the origin? What is the maximum distance?

(3) Is there a straight line with a distance of 6 between point P and the origin? If it exists, find the equation; if it does not exist, please explain the reason.

Keywords: teaching courseware of parallel lines and intersecting lines, teaching courseware of the positional relationship between two straight lines, Beijing Normal University edition seventh grade mathematics volume 2 PPT courseware, seventh grade mathematics slide courseware download, parallel lines and intersecting lines PPT courseware download, two Download PPT courseware on the positional relationship between straight lines, in .ppt format

For more information about the "Positional Relationship between Two Straight Lines, Parallel Lines and Intersecting Lines" PPT courseware, please click the "Positional Relationship between Two Straight Lines, Parallel Lines and Intersecting Lines ppt" ppt tag.

"The Positional Relationship of Two Straight Lines" Parallel Lines and Intersecting Lines PPT Courseware 4:

"Positional Relationship of Two Straight Lines" Parallel Lines and Intersecting Lines PPT Courseware 4 Thoughts and Insights 1. The necessary and sufficient condition for the two straight lines l1 and l2 to be vertical is that the product of the slopes is -1. Is this correct? Tip: Incorrect. When the slopes of the two straight lines l1 and l2 do not exist, then the two...

"The Positional Relationship of Two Straight Lines" Parallel Lines and Intersecting Lines PPT Courseware 3:

"The Positional Relationship of Two Straight Lines" Parallel Lines and Intersecting Lines PPT Courseware 3 [Course Standard Requirements] 1. Can determine whether two straight lines are parallel or perpendicular based on their slope. 2. Can find the equation of a straight line based on whether two straight lines are parallel or perpendicular. 【Core scan】 1． Use two parallel lines...

"The Positional Relationship of Two Straight Lines" Parallel Lines and Intersecting Lines PPT Courseware 2:

"The Positional Relationship of Two Straight Lines" Parallel Lines and Intersecting Lines PPT Courseware 2 Basic Review 1. Determining whether two straight lines are parallel or perpendicular (1) Suppose the slopes of the two straight lines l1 and l2 are k1 and k2 respectively, and the inclination angles are 1 and 2 respectively. Then when l1∥l2, 1=2, thus l1∥l2_. .

File Info

Update Time: 2024-09-24

This template belongs to Mathematics courseware Beijing Normal University seventh grade mathematics volume 2 industry PPT template

Preview