MTM 2 Notes
Unit 49
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Unit 49: Fundamental Geometric Constructions
Construction 1: Construct a Perpendicular Bisector of a Line Segment
1. Strike equal radius arcs from each endpoint.
2. Connect the intersection points of the arcs with a line.
3. The line is the perpendicular bisector.
Construction 2: Construct a Perpendicular to a Line Segment at a given point on the Line Segment
1. Strike an arc from the point so that it intersects the segment twice.
2. Construct the perpendicular bisector of the new segment formed by the intersection points.
MTM 2 Notes
Unit 49
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Construction 3: Construct a Line parallel to a Given Line at a Given Distance
1. Strike multiple arcs from points on the line where the radius is equal to the given distance.
2. Connect the arcs with a tangent line.
Construction 4: To Bisect a Given Angle
1. Strike an arc from the vertex of the angle.
2. Bisect the segment that results from connecting the intersection points.
MTM 2 Notes
Unit 49
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Construction 5: To Construct Tangents to a Circle from an Outside Point
1. Bisect the segment connecting the circle center and the outside point.
2. Strike an arc from the midpoint of that segment through the center of the circle.
3. Connect the outside point to the intersection points.
Construction 6: To Divide a Line Segment into a Given Number of Equal Parts
1. Draw another segment from one of the endpoints to make an angle.
2. Mark off the number of desired segments on the new segment.
3. Construct lines that are parallel to the line through the endpoints on each side of the angle through each
segment’s endpoint.
MTM 2 Notes
Unit 49
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Construction 7: To Copy a Given Triangle
Note: this can be used to copy any polygon by first dividing the polygon into sub-triangles.
1. Mark off one of the sides on a given line.
2. Strike radii from each endpoint that match the lengths of the other two sides.
Construction 8: To Copy a Given Angle
1. Connect the endpoints of the angle.
2. Copy the resulting triangle.
Construction 9: To Create an Equilateral Triangle
Note: this is useful for constructing 60 and 30 angles.
1. Mark off a segment on a line with the compass.
2. Strike arcs of that length from each endpoint.
3. Connect the intersection point to each endpoint of the segment.
MTM 2 Notes
Unit 49
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Practice:
1. Make a 1:1 scale drawing of the piece below (which is not in a 1:1 scale). All dimensions are in
millimeters.
2. Copy the quadrilateral below using only a compass and straight edge.