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Question:


animallover
Student
High School - 10th Grade

Why do think that when you get two slopes close enough to equal, the angle measure will actually disappear?

In this question, I'm kind of refering to a resource called the Geometer's Sketchpad. If you use this program, you're able to move around lines and angles. Even if u are not familiar with this program, try to picture two perpendicular lines that intersect at point E. Then imagine moving these two slopes to try to make them equal.

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Posted by animallover on Tuesday November 3, 2009 at 7:56 PM and tagged with geometry, math.

Answers:

  1. neela
    neela Teacher
    Graduate School

    eNotes Editor

    When the two slopes of the two lines are too close, the angle between the two lines becomes too close or near zero and in limit the angle between the lines is zero. Under this condition, the lines are parallel or the lines may coincide into a single line which is a special case of zero distance parallel lines.

    Let the 2 lines be y= m1*x+c1 and m2*x+c2, where m1 and m2 are the slopes of the lines and c1 and c2 are the y intercepts of the lines.

    Let C be the angle between the two lines, then

    tan C= (m2-m1)/(1+m1*m2)

    When , m2-m1 approaches zero, m1=m2 = m say and tanC also approaches zero implying, C , the angle between the lines also approaches zero.

    As long as c1 and c2 ( the y intercepts are different), and angle between the lines C=0, the lines are:

    y=m*x+c1 and

    y=m*x+c2 , and both lines are  parallel .

    When c1=c2=c say, both lines coincide into one single line , y=m*x+c.

    Hope this helps.

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    Posted by neela on Tuesday November 3, 2009 at 9:49 PM