Chapter 3 Part 1: Constructions ~ Duplicate Segment, Segment and Perpendiculars
When constructing a line segment, we use a compass and straightedge to first draw a ray or line and then a point that will serve as an endpoint of the new segment. Next, we measure the given segment with a compass and make a mark with the pencil end. Without changing the spacing of the compass, place the sharp end of the compass on the point drawn on the new line/ray, and make a mark on the line/ray. This is our line segment..
When constructing an angle, first swing an arc from the vertex of your angle. Then, swing a congruent arc from the new vertex. Return to the original angle; the drawn arc intersected the sides of the angle - measure this distance. On the new angle, place the sharp end of the compass on the intersection of the arc and ray and draw another arc. Draw a ray connecting the new vertex with the point of intersection.
When looking at a line segment, there is only one line that will pass through the midpoint that will be a constant distance between the two endpoints. This line is called the perpendicular bisector. To construct the perpendicular bisector, we first find the midpoint of the line segment and then use a compass and straightedge to draw the perpendicular line.
The shortest distance between a point not on a line and a line is along the perpendicular to the line. Constructing a perpendicular to a line uses the same process as constructing the perpendicular bisector of a line segment, but with one additional step. The first step is to swing an arc from the point and intersect the line in two places, which creates a segment that can be bisected.
When constructing an angle, first swing an arc from the vertex of your angle. Then, swing a congruent arc from the new vertex. Return to the original angle; the drawn arc intersected the sides of the angle - measure this distance. On the new angle, place the sharp end of the compass on the intersection of the arc and ray and draw another arc. Draw a ray connecting the new vertex with the point of intersection.
When looking at a line segment, there is only one line that will pass through the midpoint that will be a constant distance between the two endpoints. This line is called the perpendicular bisector. To construct the perpendicular bisector, we first find the midpoint of the line segment and then use a compass and straightedge to draw the perpendicular line.
The shortest distance between a point not on a line and a line is along the perpendicular to the line. Constructing a perpendicular to a line uses the same process as constructing the perpendicular bisector of a line segment, but with one additional step. The first step is to swing an arc from the point and intersect the line in two places, which creates a segment that can be bisected.
Construction Link 1: http://www.mathopenref.com/constcopysegment.html
Construction Link 2: http://www.mathsisfun.com/geometry/constructions.html
Notes and Powerpoints
chapter_3-part_1.pdf | |
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Homework/Classwork
chapter_3_constructions_assignment_1.pdf | |
File Size: | 23 kb |
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