Name: The 7* asic Constructions Guided Notes Included: 1. Given an segment, construct a 2 nd segment congruent to the original. (ctually not included!) 2. Given an angle, construct a 2 nd angle congruent to the original. 3. Given an angle, construct it s bisector. 4. Given a segment, construct it s perpendicular bisector 5. Given a point ON a segment/line, construct a perpendicular to the segment/line through the point. 6. Given a point NOT ON a segment/line, construct a perpendicular to the segment/line through the point. 7. Given a line & a point not on the line, construct a line parallel to the given line. solid online reference: http://www.mathopenref.com/tocs/constructionstoc.html Geometry Fall Semester
2. Construct an angle congruent to a given angle. 1. To draw an angle congruent to, begin by drawing a ray with endpoint. 2. lace the compass on point and draw an arc across both sides of the angle. Without changing the compass radius, place the compass on point and draw a long arc crossing the ray. Label the three intersection points as shown. C E 3. Set the compass so that its radius is C. lace the compass on point E and draw an arc intersecting the one drawn in the previous step. Label the intersection point F. C F E 4. Use the straightedge to draw ray F. EF C C F E
3. Construct the bisector of an angle. 1. Let point be the vertex of the angle. lace the compass on point and draw an arc across both sides of the angle. Label the intersection points and. 2. lace the compass on point and draw an arc across the interior of the angle. 3. Without changing the radius of the compass, place it on point and draw an arc intersecting the one drawn in the previous step. Label the intersection point W. W 4. Using the straightedge, draw ray W. This is the bisector of. W
4. Construct the perpendicular bisector of a line segment. Or, construct the midpoint of a line segment. 1. egin with line segment. 2. lace the compass at point. djust the compass radius so that it is more than (½). raw two arcs as shown here. 3. Without changing the compass radius, place the compass on point. raw two arcs intersecting the previously drawn arcs. Label the intersection points and. 4. Using the straightedge, draw line. Label the intersection point M. oint M is the midpoint of line segment, and line is perpendicular to line segment. M
5. Given point ON line, construct a line through, perpendicular to. 1. egin with line, containing point. 2. lace the compass on point. Using an arbitrary radius, draw arcs intersecting line at two points. Label the intersection points and. 3. lace the compass at point. djust the compass radius so that it is more than (½). raw an arc as shown here. 4. Without changing the compass radius, place the compass on point. raw an arc intersecting the previously drawn arc. Label the intersection point. 5. Use the straightedge to draw line. Line is perpendicular to line.
6. Given point, NOT ON line, construct a line through, perpendicular to. 1. egin with point line and point, not on the line. 2. lace the compass on point. Using an arbitrary radius, draw arcs intersecting line at two points. Label the intersection points and. 3. lace the compass at point. djust the compass radius so that it is more than (½). raw an arc as shown here. 4. Without changing the compass radius, place the compass on point. raw an arc intersecting the previously drawn arc. Label the intersection point. 5. Use the straightedge to draw line. Line is perpendicular to line.
7. Given a line and a point, construct a line through the point, parallel to the given line. 1. egin with point and line. 2. raw an arbitrary line through point, intersecting line. Call the intersection point. Now the tas is to construct an angle with vertex, congruent to the angle of intersection. 3. Center the compass at point and draw an arc intersecting both lines. Without changing the radius of the compass, center it at point and draw another arc. 4. Set the compass radius to the distance between the two intersection points of the first arc. Now center the compass at the point where the second arc intersects line. Mar the arc intersection point. 5. Line is parallel to line.