Constructions Flashcards

The main tools used in constructions are a ruler, compass, and protractor.

To construct a perpendicular bisector, place the compass at each endpoint of a line segment, draw arcs above and below the line, and connect the intersection points of the arcs.

To bisect an angle, place the compass on the angle's vertex, draw arcs on both arms, then draw arcs from the intersection points of the first arcs. Connect the vertex to the intersection of the second arcs.

Place the compass on the point, draw an arc that intersects the line at two points, then construct the perpendicular bisector of the segment between these two points.

Place the compass on the given point, draw arcs on either side of the point, then construct the perpendicular bisector of the segment between the arcs.

To construct a 60° angle, place the compass on a point, draw an arc, then without changing the compass width, place the compass on the arc's intersection with the line and draw another arc. Connect the point to the second arc intersection.

To construct a 90° angle, first construct a perpendicular bisector of a line segment, or use the method for constructing a perpendicular at a point on a line.

To construct an equilateral triangle, draw a line segment, then use the compass to draw arcs from each endpoint with the same radius as the segment. Connect the intersections of the arcs to the endpoints.

A locus is the set of points that satisfy a given condition, such as being a fixed distance from a point or line.

The locus of points equidistant from two points is the perpendicular bisector of the line segment joining the two points.