Perpendicular lines

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PERPENDICULAR LINES

Transcript of Perpendicular lines

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PERPENDICULAR LINES

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1. LINE BISECTORThe line bisector is a perpendicular line that passes through the

midpoint of the segment.

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First of all we need to draw a segment. We call it AB.

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STEPS:

1.Center your compass in point A, open it further from the middle of the segment AB, and draw an arc.

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STEPS:

1.Center your compass in point A, open it further from the middle of the segment AB, and draw an arc.

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1.Center your compass in point A, open it further from the middle of the segment AB, and draw an arc.

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2.Do the same from point B, where these arcs cross each other we get points 1 and 2.

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2.Do the same from point B, where these arcs cross each other we get points 1 and 2.

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3.Join 1 and 2, and this way we will get the line bisector of segment AB.

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3.Join 1 and 2, and this way we will get the line bisector of segment AB.

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3.Join 1 and 2, and this way we will get the line bisector of segment AB.

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2. PERPENDICULAR LINE TO A GIVEN RAYON ITS ENDPOINT

We say that a line is perpendicular to other line when

they intersect forming a right angle (90o).

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First of all we need to draw a ray (r) and call its endpoint A.

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STEPS:

1.Center your compass in the endpoint of the ray (A). Draw an arc with the measure you want and where this arc crosses the ray we get point 1.

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1.Center your compass in the endpoint of the ray (A). Draw an arc with the measure you want and where this arc crosses the ray we get point 1.

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2.Center your compass in point 1 and with the previous measure draw another arc. Where that arc crosses the previous one we get point 2.

2

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3.Center your compass in point 2 and with the same measure draw another arc. Where that arc crosses the first arc we have drawn, we get point 3.

3

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4.Center your compass in point 3 and with the same measure draw another arc. Where that arc crosses the last arc you have drawn, we get point 4.

4

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5.Joining point 4 with the given point A we will get the perpendicular line to the ray on its endpoint.

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5.Joining point 4 with the given point A we will get the perpendicular line to the ray on its endpoint.

r

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5.Joining point 4 with the given point A we will get the perpendicular line to the ray on its endpoint.

r

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3. PERPENDICULAR LINE TO A LINE FROM A POINT ON IT

Given a line and a point on that line, we will construct

a perpendicular line through the given point.

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First of all we need to draw a line (r) and mark a point (A) on it.

r

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STEPS:

1.Center your compass in the given point A and draw an arc with the measure you want, where the arc crosses the line we get 1 and 2.

r

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STEPS:

1.Center your compass in the given point A and draw an arc with the measure you want, where the arc crosses the line we get 1 and 2.

r

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STEPS:

1.Center your compass in the given point A and draw an arc with the measure you want, where the arc crosses the line we get 1 and 2.

r

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2.Get the line bisector between 1 and 2.

r

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2.Get the line bisector between 1 and 2.

r

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3.We get the points 3 and 4.

r

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4.Join 3 and 4, and this way we will get the perpendicular to the given line on point A.

r

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4.Join 3 and 4, and this way we will get the perpendicular to the given line on point A.

r

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4.Join 3 and 4, and this way we will get the perpendicular to the given line on point A.

r

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4. PERPENDICULAR LINE TO A LINE FROM AN EXTERNAL POINT

Given a line and a point outside that line, we will construct

a perpendicular line through the given point.

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First of all we need to draw a line (r) and mark an external point (A). It doesn’t matter where the point is, below or above the line, the steps will be the same.

r

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STEPS:

1. Center your compass in the given point A and draw an arc which crosses the given line r in two points called 1 and 2.

r

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STEPS:

1. Center your compass in the given point A and draw an arc which crosses the given line r in two points called 1 and 2.

r

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STEPS:

1. Center your compass in the given point A and draw an arc which crosses the given line r in two points called 1 and 2.

r

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2.Get the line bisector between 1 and 2.

r

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2.Get the line bisector between 1 and 2.

r

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3.We get the points 3 and 4.

r

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4.Join 3 and 4, and this way we will get the perpendicular to the given line on point A.

r

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4.Join 3 and 4, and this way we will get the perpendicular to the given line on point A.

r

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4.Join 3 and 4, and this way we will get the perpendicular to the given line on point A.

r