GEOGEBRA #5
Name______________________________________
Go to www.geogebra.org , click on DOWNLOAD, then APPLETSTART. Go to VIEW-> and deselect the AXES (no grid or axes today)
Save all 3 constructions by going to SAVE AS… -> COMPUTER-> PUBLIC-> CLASS FOLDER-> KSCOTT-> select your class period.
#4: Construct the perpendicular bisector of a segment http://geogebrawiki.wikispaces.com/Bisect-Segment
Draw line segment
AB
Draw a third point, C, on the line segment AB about 2/3 of the way from A to B. (AC must be bigger than 1/2 of AB)
Draw circle with radius AC and center A by clicking on points A, C and A. Make this circle red
Draw circle with radius AC and center B by clicking on points A, C and B. Make this circle blue
Draw point D by clicking on top intersection point of the red and blue circles
Draw point E by clicking on bottom intersection point of the red and blue circles
Draw line through D and E by clicking on points D and E. ( DE is the perpendicular bisector of
Draw point F by clicking on intersection point of
DE
and
AB )
AB .
Check the construction by using tools 8C to find the lengths of AF and BF. Then use tool 8A to find the measure of AFD
Verify that the construction by clicking and dragging the endpoints
AB
to change its size.
Save construction. File -> Save As.. (Save in CLASS FOLDER under KSCOTT with your name and the number 4 )
DE . Find the distance from G to each of the endpoints A & B. What do you
observe about these distances? They are the ____________. Use this information to fill in the theorem below:
Now, place any point, G, on the perpendicular bisector
Any point located on the perpendicular bisector of a segment is _________distance to the ____________ of the bisected segment
#5: Construct the angle bisector of a given angle: http://geogebrawiki.wikispaces.com/Bisect-Angle
Using the ray tool, Draw
BAC
by making two rays that share a common endpoint, A.
Draw circle with radius AC and center at A by clicking A, C and then A. Make this circle RED.
Draw point D by clicking on the intersection point of the red circle and AB
Points C and D will now be equidistant from A
Draw circle with radius CD and center C by clicking on points C, D, then C. Make this circle BLUE
Draw circle with radius CD and center D by clicking on points C, D, then D. Make this circle GREEN
Draw point E by clicking on either intersection point of the BLUE and GREEN circles
Draw a ray from A through E by clicking on A and E. AE is now the angle bisector of CAD
Check your construction by measuring angles DAE and EAC
Verify your construction by clicking and dragging points A, C, or D to change the size of the angle.
Open a text box and write a paragraph proof that will verify why this construction assures that AE is the angle bisector of
BAC
(Consider drawing line segments CE and DE and proving congruent triangles)
Save construction. File -> Save As.. (Save in CLASS FOLDER under KSCOTT with your name and the number 5 )
Now, place a point, F, anywhere on the angle bisector AE . Use the perpendicular line tool (4A) to construct a line that is perpendicular to
AB from point F (click on point F, then select AB ) Now construct another perpendicular line from F to AC . Place point G at the
intersection of AE & AB . Now place point H at the intersection of AE & AC . Find the lengths of FG and FH using the distance tool (8C)
Any point on the angle bisector of segment is __________distance to the _________of the bisected angle.