Download Geometry Construction Project

Geometry Construction Project Rubric
Ms. Chaney ~ East Paulding High School
For an “A” (90-100%) grade:
 20 to 24 constructions
 all are defined/described by a conjecture or
 a compass is used
theorem
 no freehand lines or freehand arcs
 a straightedge is used
 white paper is used
 the drawing is clean
 all constructions are in a three-ring binder
 compass “marks” and arcs are evident
For a “B” (80-89%) grade:
 15 to 19 constructions
 all are defined/described by a conjecture
 a compass is used
or theorem
 no freehand lines or freehand arcs
 a straightedge is used
 white paper is used
 the drawing is clean
 all constructions are in a three-ring binder
 compass “marks” and arcs are evident
For a “C” (70-79%) grade:
 10 to 14 constructions
 all are defined/described by a conjecture
 a compass is used
or theorem
 no freehand lines or freehand arcs
 a straightedge is used
 white paper is used
 the drawing is clean
 all constructions are in a three-ring binder
 compass “marks” and arcs are evident
Anything less than the above performances will result in a failing “F” grade and CANNOT be submitted
for the optional assignment!
All constructions must be in a THREE-RING BINDER. There are no exceptions! The three ring
binder will have a title page, this rubric and the constructions list. Highlight the names of the
constructions you have drawn. Please number each page of your project. Place the
constructions in the order they are on the sheet in this packet. Each construction should be
followed immediately with its construction write-up.
This project is due on: TUESDAY, OCTOBER 6, 2015 DURING YOUR ASSIGNED CLASS TIME. (It will
be received ONLY on or before the due date!! NO EXCEPTIONS)
REMEMBER!!!
This is your project!! YOU MAY NOT RECEIVE ANY OUTSIDE HELP (this includes a tutor).
As always, I am available to assist you, but this must be your work.
Geometry Constructions
1.
Subtracting Line Segments
2.
Adding Angles
3.
Constructing Congruent Angles
4.
Square
5.
Rectangle
6.
Rhombus
7.
Pentagon
8.
Octagon
9.
Isosceles Acute Triangle
10.
Isosceles Right Triangle
11.
Isosceles Trapezoid
12.
Constructing a Line Perpendicular through a Point Not On the Line
13.
Constructing a Line Parallel to Another Line
14.
Two Parallel Lines with Alternate Exterior Angles
15.
Two Parallel Lines with Alternate Interior Angles
16.
Two Parallel Lines with Corresponding Angles
17.
Two Parallel Lines with Same Side Exterior Angles
18.
Two Parallel Lines with Same Side Interior Angles
19.
Bisecting an Angle (Angle Bisector Conjecture)
20.
Perpendicular Bisector of a Segment
21.
Constructing a Triangle from Three Line Segments
22.
Constructing a 30-60-90 Triangle
23.
Constructing a 45-45-90 Triangle
24.
Constructing the Perpendicular Bisector of a Triangle
25.
Constructing the Altitude of a Triangle
26.
Constructing the Angle Bisector of a Triangle
Geometry Construction Write-Up (EXAMPLE)
Use a separate plain (unlined) white sheet of 8.5 * 11 paper for your construction.
This sheet is for the following:
Name of Construction:
Constructing a 45-45-90 Triangle
Method: (Explain how you made the construction)
I drew two points on the paper and connected them with a ruler to make AB . (By postulate 2.1)
Next, I constructed a perpendicular bisector of AB by placing my compass at A and adjusting my compass to a
1
AB and drew arcs below and above AB (definition on a line segment). Using the
2
same compass setting, I placed the compass at B and drew arcs above and below AB so that they intersected the
previously drawn arcs. I labeled these points C and D. Using a straightedge to draw CD . I labeled the point
where AB intersected CD as point E. E is the midpoint of AB , and CD is a perpendicular bisector of AB by
theorem 2.1 and the definition of a perpendicular line. After drawing CD with my straightedge (def. of a line) I
labeled AEC as 90 , by the definition of a perpendicular line. CD is perpendicular to AB and by the definition
of perpendicular lines we know that they form a right angle. Thus, AEC is a right angle and the measure of
AEC is 90 .
width that was greater than
Next, I bisected AE by placing my compass at A and adjusting my compass to a width that was greater than
1
AE and drew arcs below and above AE (definition on a line segment). Using the same compass setting, I
2
placed the compass at E and drew arcs above and below AE so that they intersected the previously drawn arcs. I
labeled these points G and H. Using a straightedge to draw GH . I labeled the point where AE intersected GH as
point F. F is the midpoint of AE , and GH is a bisector of AE by theorem 2.1 and the definition of a
perpendicular line. After drawing GH with my straightedge (def. of a line) I labeled EFG as 90 . GH is
perpendicular to AE and by the definition of perpendicular lines we know that they form a right angle. Thus,
EFG is a right angle and the measure of EFG is 90 .
After that I constructed an angle bisector for AEC angle. To do this I placed the sharp point of my compass on
the vertex of AEC and drew an arc intersecting both sides of AEC , I labeled these intersection points I and J.
With the compass on point I, I drew an arc in the interior of AEC . Keeping the same compass setting, I placed
the compass on point J and dew an arc the intersected the arc from point I, I then labeled the point K. Next, I drew
a ray connecting point E thru point K by the definition of a ray. I then extended EK until it intersected GH . I
labeled that point L. Therefore, by the definition of an angle bisector I know that FEL is a 45 degree angle.
Now, by Theorem 4.1 I know LFE is 180 degrees. Thus, FLE must be a 45 degree angle as well, by the
triangular sum theorem. Hence, creating a 45-45-90 degree triangle.
GEOMETRY CONSTRUCTION WRITE-UP
Name of Construction (on page _____):
Method: (Explain how you made the construction)
Page _______