Geometry SOL G.4 Constructions Mrs. Grieser Name Date Block Constructions Grab your compass and straight edge - it s time to learn about constructions!! On the following pages you will find instructions on how to do the following constructions: Constructing a Segment Congruent to a Given Line Segment Constructing the Perpendicular Bisector of a Line Segment Constructing a Perpendicular Line to a Given Line at a Point on the Line Constructing a Perpendicular Line to a Given Line from a Point Not on the Line Constructing an Angle Congruent to a Given Angle Constructing the Bisector of a Given Angle Constructing a Parallel Line to a Given Line through a Point Not on the Line You are to practice each one of these constructions 4 times with each set. Use another piece of paper as necessary. Each one should use slightly different measurements. So for #1, the line segments used should all be of different length. Practice more by drawing your own segments or angles if you need to! When you have finished practicing, you will do the project described on the last page of the packet. Be creative and have fun with it! For more practice with constructions, see the following web page: http://www.mathopenref.com/constructions.html
Geometry SOL G.4 Constructions Mrs. Grieser Page 2 Constructing a Segment Congruent to a Given Line Segment 1. Start with a line segment PQ to copy. 2. Mark a point R that will be one endpoint of the new line segment. 3. Set the compass point on the point P of the line segment to be copied. Adjust the compass width to the point Q. The compass width is now equal to the length of the line segment PQ. 4. Without changing the compass width, place the compass point on the point R on the line you drew, and draw an arc where the other endpoint will be. Pick a point S on the arc that will be the other endpoint of the new line segment. 5. Pick a point S on the arc that will be the other endpoint of the new line segment. Draw a line from R to S. The line segment RS is equal in length (congruent to) the line segment PQ. Practice: Copy the line segments
Geometry SOL G.4 Constructions Mrs. Grieser Page 3 Constructing the Perpendicular Bisector of a Line Segment: 1. Begin with line segment XY. 2. Place the compass at point X. Adjust the compass radius so that it is more than ½ the length of XY. Draw two arcs as shown here. 3. Without changing the compass radius, place the compass on point Y. Draw two arcs intersecting the previously drawn arcs. Label the intersection points A and B. 4. Using the straightedge, draw line AB. Label the intersection point M. Point M is the midpoint of line segment XY, and line AB is perpendicular to line segment XY. Practice: Bisect the line segments
Geometry SOL G.4 Constructions Mrs. Grieser Page 4 Constructing a Perpendicular Line to a Given Line at a Point on the Line: 1. Begin with line k, containing point P. 2. Place the compass on point P. Using an arbitrary radius, draw arcs intersecting line k at two points. Label the intersection points X and Y. 3. Place the compass at point X. Adjust the compass radius so that it is more than ½ the length of XY. Draw an arc as shown here. 4. Without changing the compass radius, place the compass on point Y. Draw an arc intersecting the previously drawn arc. Label the intersection point A. 5. Use the straightedge to draw line AP. Line AP is perpendicular to line k. Practice: Construct a perpendicular line through the given point on the line segment
Geometry SOL G.4 Constructions Mrs. Grieser Page 5 Constructing a Perpendicular Line to a Given Line from a Point Not on the Line: 1. Begin with point line k and point R, not on the line. 2. Place the compass on point R. Using an arbitrary radius, draw arcs intersecting line k at two points. Label the intersection points X and Y. 3. Place the compass at point X. Adjust the compass radius so that it is more than ½ the length ofxy. Draw an arc as shown here. 4. Without changing the compass radius, place the compass on point Y. Draw an arc intersecting the previously drawn arc. Label the intersection point B. 5. Use the straightedge to draw line RB. Line RB is perpendicular to line k. Practice: Draw a line through the point perpendicular to the segment
Geometry SOL G.4 Constructions Mrs. Grieser Page 6 Constructing an Angle Congruent to a Given Angle: 1. To draw an angle congruent to A, begin by drawing a ray with endpoint D. 2. Place the compass on point A and draw an arc across both sides of the angle. Without changing the compass radius, place the compass on point D and draw a long arc crossing the ray. Label the three intersection points as shown. 3. Set the compass so that its radius is BC. Place the compass on point E and draw an arc intersecting the one drawn in the previous step. Label the intersection point F. 4. Use the straightedge to draw ray DF. EDF BAC Practice: Copy the angles a) b)
Geometry SOL G.4 Constructions Mrs. Grieser Page 7 Constructing the Bisector of a Given Angle: 1. Let point P be the vertex of the angle. Place the compass on point P and draw an arc across both sides of the angle. Label the intersection points Q and R. 2. Place the compass on point Q and draw an arc across the interior of the angle. 3. Without changing the radius of the compass, place it on point R and draw an arc intersecting the one drawn in the previous step. Label the intersection point W. 4. Using the straightedge, draw ray PW. This is the bisector of QPR. Practice: Bisect the angles
Geometry SOL G.4 Constructions Mrs. Grieser Page 8 Constructing a Parallel Line to a Given Line through a Point Not on the Line: 1. Start with a line segment PQ and a point R off the line. 2. Draw a transverse line through R and across the line PQ at an angle, forming the point J where it intersects the line PQ. The exact angle is not important. 3. With the compass width set to about half the distance between R and J, place the point on J, and draw an arc across both lines. 4. Without adjusting the compass width, move the compass to R and draw a similar arc to the one in the previous step. 5. Set compass width to the distance where the lower arc crosses the two lines. 6. Move the compass to where the upper arc crosses the transverse line and draw an arc across the upper arc, forming point S. 7. Draw a straight line through points R and S. The line RS is parallel to the line PQ. Practice: see back
Geometry SOL G.4 Constructions Mrs. Grieser Page 9 Practice: Draw a line through the point parallel to the segment
Geometry SOL G.4 Constructions Mrs. Grieser Page 10 Putting It All Together Create a drawing (abstract or otherwise), that uses all the constructions in this packet. You may use this paper for a draft, and another for the final drawing. Each construction must be used at least TWICE, but may be used more than twice. Label each construction (such as congruent segment or bisected angle ) Use color, have fun, and be creative!