Download Challenge One

Challenge One
Name_____________Class_______
Use only a compass and straightedge to complete this challenge. Do Not Erase any
construction marks.
Engineers are constructing a walkway into the park that is the perpendicular bisector to Elm
Street. Construct the walkway as it will appear on a map of the park.
Will the sandbox need to be moved? _________
Explain in detail why this is true. ______________________________________________
_______________________________________________________________________
_______________________________________________________________________
Sandbox
A
Elm Street
B
The diagram below shows XY which is the perpendicular bisector of AB . One compass setting
was used to construct four arcs which were needed to construct bisector XY . On which two
points was the point of the compass placed to make these important arcs? _______________
Which line segments in the picture below are not parts of the construction for the
perpendicular bisector? Make sure to name them using correct geometric notation.
_______________________________________________________________
A
X
Y
B
Challenge Two
Name_____________Class_______
Use only a compass and straightedge to complete this challenge. Do Not Erase any
construction marks.
Construct an angle congruent to PQR . Correctly label the copy of PQR .
1.
Write the correct congruency statement. ________________________________
P
Q
2.
R
Construct an angle congruent to ACB . Correctly label the copy of ACB . Write the
correct congruency statement for these two angles. _______________________
A
C
3.
B
Construct an angle bisector of angle BDC.
Correctly mark the drawing showing the new
congruent angles then write the congruency
statement for those angles.
.________________________
A
B
C
D
Challenge Three
Name_____________Class_______
Use only a compass and a straight edge to complete this challenge. Do Not Erase any
construction marks.
The diagram below shows a square patio. Construct the angle bisectors of
ABD and BDC . Extend each bisector to intersect the square at two points.
A
B
C
D
Do the bisectors intersect at the center of the square? ___________
Explain how you know you’ve found the center?
_______________________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
What fraction of the square does each angle bisector create?
What geometric figures are formed inside the square by the angle bisectors?
_____________________
Challenge Four
Name_____________Class_______
Use only a compass and a straight edge to complete this challenge. Do Not Erase any
construction marks.
1.
Construct a line perpendicular to line n through point S. Write a statement about the
perpendicular relationship between the two lines. _____________________________
S
n
2.
Momma Duck needs to get to the river where her babies are swimming. Construct a path
for Momma Duck that will be the shortest route for her to get to the edge of the river.
Why is this line the shortest route to the river? ____________________________
_________________________________________________________________
River
Challenge Five
Name_____________Class_______
Use a compass and a straight edge to complete the constructions below. Do Not Erase any
construction marks
1.
A line parallel to line AB through point L. Write the correct statement about the parallel
relationship between these two lines. ______________________________________
L
A
2.
B
A line parallel to side CB through point A. You may extend thee length of any line
segments in order to make the construction easier to perform. Write the correct
statement regarding the parallel relationship between the two lines.
_______________________________
A
B
C
Challenge Six
Name_____________Class_______
Use a compass and a straight edge to complete this challenge. Do Not Erase any construction
marks.
Construct line CD as a perpendicular bisector to line AB. Label the point of intersection point J.
Construct line RT as a perpendicular bisector to line segment CJ. Mark your drawing indicating
the right angles you have just constructed.
What is the relationship between line AB and line RT? ______________________________
Explain why this relationship exists. ___________________________________________
_______________________________________________________________________
_______________________________________________________________________
A
B
Challenge Seven
Name_____________Class_______
A “regular polygon” is defined as any multisided figure where
all sides are the same length and all angles have the same
measure.
Draw line segment DE. Draw a perpendicular bisector of line segment DE. Name the bisector
line segment BC. Name the point of intersection point Y. Use this construction and the
knowledge you have gained in this unit to construct a regular octagon. As with all other
challenges, you will only be allowed to use your compass and straight edge to complete this
challenge.
Do not erase any construction marks.
Constructions Challenge
This counts as a major test grade.
Instructions and Suggestions.
Due Date Monday February 23
All seven challenges must be completed by each student. Students may work together within
their teams to generate ideas and help each other, but each construction must be completed
individually. All work will be done outside of class and can be completed in any order and should
be turned in as it is completed. You may use your notes, your textbook, or any other resources
with the exception of your teacher for assistance. Each questions asked of the teacher will
cost a total of 5 points off of your total grade.
This assessment is worth a total of 100 points. Each challenge counts for a total of 16 points.
These points will be earned after completing the required constructions, answering the
questions and other written responses as well as any geometric notations such as congruency
statements, parallel statements, etc.
Use the following suggestions to make the best possible grade.
 Do not erase any construction marks.
 It is OK to extend any line or line segment using your straight edge if it is too short to
complete your construction.
 Give detailed and complete responses when answering a question.
 Make sure all work is neat and easy to read.
 Make sure to always use correct symbols and other accurate geometric notation.
 Keep in mind that constructions are created using arcs which are parts of circles.
Therefore diameters and radii of circles are important to consider when answering
questions.
 Creation of congruent triangles is important to each construction.
 Rely on each other, your notes and your own logic to help you respond to the challenges.
 Make sure you read each challenge carefully and do all required parts of
each construction. Be very careful not to overlook any information
provided for you or any required answers in any of the challenges.

You may check each others’ work for completeness and accuracy before turning it in. Any
answers that are copies of other student work will receive no credit. Your work must
be your own. I have to know what you are thinking, not someone else.