Line Bisectors and Angle Bisectors
Perpendicular line (point not belonging to line)
- Select the COMPASS tool (Window 5). Then click on the segment AB (it represents the length opening of the compass) and on E (represents the sharp end of the compass).
- Select the INTERSECT tool (Window 3) and mark F and G. They are points of intersection of the circle with the line.
- Select the COMPASS tool (Window 6). Then click on point F and point G (it represents the length opening of the compass) and again on point F (it represents the sharp end of the compass). After that, click on point G and point F (it represents the length opening of the compass) and again on G (it represents the sharp end of the compass).
- Select the INTERSECT tool (Window 3) and mark a point H, point of intersection of the last two circles.
-Select the LINE tool (Window 4) and click on point E and point H. The intended perpendicular line will appear. Let us analyse it.
- Select the INTERSECT tool (Window 3) and mark point I, point of intersection of points h and g.
- Select the ANGLE tool (Window 9). Click on points E, I and C to mark the angle EIC (the vertex of the angle will always be the second point clicked). What is the measurement of this angle?
- Select the SHOW / HIDE OBJECT tool (Window 7) and hide the circles, points H, F and G, leaving only the lines and point E.
-Select the RELATION tool (Window 8) and click on the two lines. What happens when you follow all the steps above?
- Select the MOVE tool (Window 1). Move either point E or line g. What can you see?
Perpendicular line (point not belonging to the line)
Perpendicular line (point belonging to line)
-Select the COMPASS tool (Window 5). Then click on the segment AB (it represents the length opening of the compass) and on E (it represents the sharp end of the compass).
- Select the INTERSECT tool (Window 3) and mark the intersections F and G of the circle with the line g.
- Select the COMPASS tool (Window 6). Then click on point F and point G (it represents the length opening of the compass) and again on point F (it represents the sharp end of the compass). After that, click on point G and point F (it represents the length opening of the compass) and again on G (represents the sharp end of the compass).
- Select the INTERSECT tool (Window 3) and mark a point H, point of intersection of the last two circles.
-Select the LINE tool (Window 4) and click on point E and point H. The intended perpendicular line will appear.
-Select the ANGLE tool (Window 9). Click on points H, E and C to mark the angle HEC (the vertex of the angle will always be the second point clicked). What is the measurement of this angle?
- Select the SHOW / HIDE OBJECT tool (Window 7) and hide the circles, points H, F and G, leaving only the lines and point E.
-Select the RELATION tool (Window 8) and click on the two lines. What happens when you follow all the steps above?
- Select the MOVE tool (Window 1). Move either point E or line g. What can you see?
Perpendicular line (point belonging to line)
Line Segment Bisector
- Select the COMPASS tool (Window 6). Then click on point A and point B (it represents the length opening of the compass) and again on point A (it represents the sharp end of the compass). After that click on point B and point A (it represents the length opening of the compass) and again on B (it represents the sharp end of the compass).
- Select the option INTERSECT (Window 3) and mark C and F, which are the intersections between the two circles.
-Select the LINE tool (Window 4) and click on C and D. This is the aimed line bisector.
- Select the INTERSECT (Window 3) and mark E, which is the intersection of g with segment AB.
- Select the SHOW/HIDE OBJECT tool (Window 7) and hide the circles, points C and D, leaving only the lines and point E.
- Select the MOVE tool (Window 1) Move point A or B. What can you see?
Drawing the Line segment Bisector
Analysis 1
How do you know that any point of the line has the same distance to A and to B?
Analysis 2
How do you know that the angle AEC measures 90º?
Angle Bisector with visible vertex
-Select the COMPASS tool (Window 5). Then click on the segment AB (it represents the length opening of the compass) and on C (it represents the sharp end of the compass).
- Select the INTERSECT tool (Window 3) and mark F and G. They are the points of intersection between the circle and the rays (Half-lines) that form the angle.
- Select the COMPASS tool (Window 6). Then click on the segment AB (it represents the length opening of the compass) and on G (it represents the sharp end of the compass). Then click on segment AB (it represents the length opening of the compass) and on F (It represents the sharp end of the compass).
- Select the INTERSECT tool (Window 3) and mark a point H, point of intersection of the last two circles.
-Select the RAY (HALF-LINE) tool (Window 6) and click on C and H. This is the intended angle bisector.
- Select the SHOW/HIDE OBJECT tool (Window 7) and hide the circles and the points F and G.
-Select the ANGLE tool (Window 7). Click on points D, C and H to mark the angle HEC (the vertex of the angle will always be the second point clicked). Also measure the HCE angle. What can you see?
- Select the MOVE tool (Window 1). Move either point E or line d. What can you see?