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Pattern

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Geometric Constructions

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Dividing a Line Segment into Equal Parts

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1. Draw a non-collinear line from one end of the segment. 2. Set your compass to a convenient width and make marks along the new line, with each arc further than the last. 3. Connect the last arc to the other end of the segment and draw lines from each intersection on the new line to this end; the segment will now be divided into equal parts.

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Angle Bisector

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1. With the compass point on the angle vertex, draw an arc that intersects both sides of the angle. 2. Without changing the compass width, draw arcs from the points where the first arc crossed the angle's sides. 3. Draw a line from the vertex to the point where the two new arcs intersect; this line is the angle bisector.

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Copying a Triangle

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1. Draw the base of the new triangle equal to one side of the original triangle. 2. Copy the angles from the original triangle using the angle bisector steps at each base end. 3. Where the two copied angles meet is the third point of the triangle; connect the points to complete the triangle copy.

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Construct a Perpendicular Line from a Point on a Line

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1. Place the compass on the given point, and draw an arc that intersects the line at two points. 2. Without changing the compass width, draw arcs from both intersection points. 3. Draw a line from the original point through the point where the two arcs intersect outside the line; this is the perpendicular line.

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Constructing a Parallel Line through a Point

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1. Draw a line from the given point to any point on the given line. 2. Construct a perpendicular bisector of the line you just drew. 3. Draw a line through the given point; this line should be parallel to the original line by following the same angle created by the bisector.

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Construct a Perpendicular Line from a Point outside a Line

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1. Place the compass on the given point and draw an arc crossing the line at two points. 2. From each intersection point, draw two arcs that intersect each other using the same compass width. 3. Draw a line from the given point through the point where the arcs intersect; this will be perpendicular to the original line.

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Inscribe a Circle in a Triangle

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1. Bisect two angles of the triangle. 2. The point where the bisectors intersect is the center of the inscribed circle (incircle). 3. Place the compass at the center and adjust it to reach one side of the triangle, then draw the circle; it should touch all three sides.

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Perpendicular Bisector

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1. Place the compass at one end of the line segment and draw an arc above and below the line. 2. Without changing the compass width, repeat from the other end of the line segment. 3. Draw a line where the arcs intersect; this line is the perpendicular bisector.

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Construct a Square

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1. Draw a line segment that will be one side of the square. 2. Construct perpendicular lines at each endpoint of the segment. 3. From each endpoint, mark off on the perpendicular lines a length equal to the original line segment and connect these points to form a square.

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Circumscribe a Circle Around a Triangle

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1. Perpendicular bisect two sides of the triangle. 2. The point where the bisectors intersect is the center of the circumscribed circle. 3. Place the compass at the center with a radius reaching any vertex, and draw the circle; it should pass through all three vertices.

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