
Angle Bisector



Construction
1. Using the Compass
button draw an arc centered at A and create intersection
points F and G.
2. With F and G as centers, draw arcs with equal radii that
intersect at J.
3. Draw a ray through A and J. This is the desired angle
bisector. Verification
and proof
A. Verify the above by
measuring the angles with the
compass.
B. Prove the ray AJ is an angle bisector, using logical
geometric arguments.


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Dividing
a Segment into Equal Parts 



Construction
1. Draw a ray with A as center.
With the compass, mark off equal segments starting at A: AE=EF=FH=HC.
2. Draw CB. Using the parallel button draw parallels to CB through
points E,F,H.
The intersection points of the parallels with AB, divide AB into
four equal parts.
Verification
and proof
A. Verify the above by
measuring the segments.
B. Prove the segments are equal using logical geometric arguments.

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Parallel to a Given Line 



Construction
1. With C as center draw an arc that intersects the line at points E
and F.
2. Draw lines through CE and CF. With C as center draw an arc which
intersects CE at I and CF at K. With I and K as centers draw equal
arches that intersect at L.
3. Draw a line through C and L. This is the desired parallel.
Verification
and proof
A. Verify the above by measuring the appropriate angles.
B. Prove the lines are parallel using logical geometric arguments.

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Perpendicular Bisector to a Given Segment




Construction
1. Using
the compass button, draw an arc with E as center that intersects AB
at points G and F.
2. With the intersection points
G and F as centers, draw equal arcs that intersect at the other side
of AB at point J. Connect E to J. This is the desired perpendicular.
Verification
and proof
A. Verify the above by measuring the
angles EDF and EDG.
B. Prove CJ is a perpendicular using logical geometric arguments.

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Constructing
an Angle that is Equal to a Given One 



Construction
1. With
A as center draw an arc that intersects the angle sides at points E
and F.
2. Draw ray GH.
3. With G as center draw an arc
with the same radius as before that intersects GH at point J.
4. With J as center draw an arc
with radius EF intersecting the previous arc at point K.
Draw GK. Angle HGK will equal angle BAC.
Verification
and proof
A. Verify the above by
measuring both angles.
B. Prove the angles are equal
using logical geometric arguments.

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Angles Between Lines 



Construction
1. Draw
line AB and then line CD parallel to AB. Draw transversal EF.
Measure and mark all the formed angles. Find all vertical angles,
supplementary angles and corresponding angles.
2. Explore connections between the angles when the line EF is moved,
by dragging points E or F.
3. Explore connections between
the angles when the line AB is moved, by dragging point B so that
the lines are not parallel. 
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