Download Constructions project

Common Geometry Construction Project Rubric
GSE Geometry – Howard High School
Constructions Part I
For an “A” (90-100%) grade:
24 - 27 constructions
all are defined/described by a conjecture or theorem
a compass is used
a straightedge is used
no freehand lines or freehand arcs
the drawing is clean
white paper is used
compass “marks” and arcs are evident
all constructions are in a three-ring binder
For a “B” (80-89%) grade:
21 – 23 constructions
all are defined/described by a conjecture or theorem
a compass is used
a straightedge is used
no freehand lines or freehand arcs
the drawing is clean
white paper is used
compass “marks” and arcs are evident
all constructions are in a three-ring binder
For a “C” (70-79%) grade:
19 to 22 constructions
all are defined/described by a conjecture or theorem
a compass is used
a straightedge is used
no freehand lines or freehand arcs
the drawing is clean
white paper is used
compass “marks” and arcs are evident
all constructions are in a three-ring binder
Anything less than the above performances will result in a failing “F” grade (50 percent or less).
Materials needed for this assignment:
A compass
A ruler
A 3-Prong Folder
All constructions must be in a 3-PRONG FOLDER. There are no exceptions! 3-prong folder 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: MONDAY, MARCH 6, 2017 DURING YOUR ASSIGNED CLASS TIME. (It will be received ONLY
on or before the due date!! NO EXCEPTIONS)
Geometry Constructions
1.
Copying a Segment
2.
Copying an Angle
3.
Construct line tangent to Circle
4.
Rectangle
5.
Rhombus
6.
Pentagon
7.
Square inscribed in a circle
8.
Triangle inscribed in a circle
9.
Hexagon inscribed in a circle
10.
Isosceles Acute Triangle
11.
Isosceles Right Triangle
12.
Isosceles Trapezoid
13.
Constructing a Line Perpendicular through a Point Not On the Line
14.
Constructing a Line Parallel to Another Line
15.
Two Parallel Lines with Alternate Exterior Angles
16.
Two Parallel Lines with Alternate Interior Angles
17.
Two Parallel Lines with Corresponding Angles
18.
Two Parallel Lines with Same Side Exterior Angles
19.
Two Parallel Lines with Same Side Interior Angles
20.
Bisecting an Angle (Angle Bisector Conjecture)
21.
Perpendicular Bisector of a Segment
22.
Constructing an Equilateral Triangle
23.
Constructing a 30-60-90 Triangle
24.
Constructing a 45-45-90 Triangle
25.
Constructing the Perpendicular Bisector of a Triangle
26.
Constructing the Altitude of a Triangle
27.
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 _______
Constructions Graded Practice
Constructions Part II
Each construction is worth 10 points each. This Construction Practice Assignment
should be located behind your 27 constructions/write ups in your 3 prong folder.
Copy the following Angles and line segments using a compass and a straight edge.
Construct a bisector for each of the following angles.
Construct a perpendicular bisector and a parallel line for each of the following line
segments.