GEOGEBRA #6
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.
#1 Constructing 2 congruent triangles using SSS http://geogebrawiki.wikispaces.com/Triangle-Copy
Use the segment tool to draw a triangle ∆𝐴𝐵𝐶. Right-click to change AB (red), segment AC (blue) and segment BC (green)
Draw a line. Use right-click to rename D -> P and to hide point E.
Draw a RED circle whose radius is ̅̅̅̅
𝐴𝐵 and center P by clicking on points A, B and then move the circle to point P
Draw point D by clicking on intersection point of the red circle and the line from P.
Draw circle f with radius ̅̅̅̅
𝐴𝐶 and center P by clicking on points A, C, then P. (right-click to change circle color to blue)
Draw circle g with radius the segment ̅̅̅̅
𝐵𝐶 and center D by clicking on points B, C, then D. (right-click to change color to green)
Draw point F by clicking on top intersection point of circles f and g. (look for intersection of the blue and green circles)
Draw one new triangle side by clicking on points P and D. (right-click to change the color to red)
Draw another new triangle side by clicking on points D and F. (right-click to change the color to green)
Draw the 3rd new triangle side by clicking on points P and F. (right-click to change the color to blue)
Use the measure tool to identify the lengths of each side of both triangles. Verify 3 pairs of corresponding congruent sides.
Click and drag the vertices of ∆𝐴𝐵𝐶 to change each side length. The lengths of the sides of ∆𝑃𝐷𝐹 should match
Save construction. File -> Save As.. (Save in CLASS FOLDER under KSCOTT with your name and the number 1 )
#2: Construct congruent angles http://geogebrawiki.wikispaces.com/Angle-Copy
Using the ray tool, Draw
BAC
by making two rays that share a common endpoint, A. Measure the angle using
Draw a line that does not intersect your angle. Right-click to rename D -> P
Draw a red circle whose radius is ̅̅̅̅
𝐴𝐵 with center A by clicking on points A, B and then move the circle to point A.
Draw point D by finding the intersection point of the red circle and ray AC (move point C so that it is NOT the intersection point)
Draw a blue circle whose radius is ̅̅̅̅
𝐴𝐵 with center P by clicking on points A, B and then move the circle to point P.
Draw point F by finding the intersection point of the blue circle & ray PE (move point E so that it is NOT the intersection point)
Draw a green circle whose radius is ̅̅̅̅
𝐵𝐷 with a center F by clicking on points B, D, then move the circle to point F.
Draw point G by finding the intersection of the blue and green circles.
Finish the new angle by forming a ray PG
Measure the angle by clicking on points F, P and G.
Check your construction by dragging points A, B and C to change size of first angle and points P and E to move line.
Save construction. File -> Save As.. (Save in CLASS FOLDER under KSCOTT with your name and the number 2 )
#3: 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 A 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 AMD
Verify that the construction by clicking and dragging the endpoints
AB
to change its size.
Open a text box and write a paragraph proof that will verify why this construction assures that
AB
DE is the perpendicular bisector of
(Discuss how the compass tool helps set up the perpendicular bisector theorem )
Save construction. File -> Save As.. (Save in CLASS FOLDER under KSCOTT with your name and the number 3 )
#4: 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 C. 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
(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 4 )
BAC