NEST+m Geometry
Midterm Exam
Short Answer – Friday, January 22, 2010
Name (please print): _____________________________________
The declaration below should be signed when you have completed the examination.
I do hereby affirm, at the close of this examination, that I had no unlawful knowledge of the questions
or answers prior to the examination and that I have neither given nor received assistance in answering
any of the questions during the examination.
_______________________________________
Student Signature
________________
Date
Geometry Reference Sheet
Volume: Cylinder: V = Bh, where B is the area of the base
Pyramid: V =
1
3
Bh, where B is the area of the base
Right Circular Cone: V =
Sphere:
Lateral Area:
Surface Area:
V=
1
3
Bh, where B is the area of the base
4 3
πr
3
Right Circ. Cylinder: L = 2πrh
Right Circ. Cone:
L = πrl, where l is slant height
Sphere:
SA = 4πr2
2
Midterm - Part 2, Short Answer questions: Each correct answer will receive 5 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc.
For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit.
Write an equation of the line that passes through the point (6,5) and is perpendicular
to the line whose equation is 2 x  3 y  11.
1
2
The endpoints of PQ are P(-3,1) and Q(4,25). Find the length of PQ .
3
Using a compass and straightedge, construct the angle bisector of ABC shown
below. [Leave all construction marks.]
3
4
5
In the diagram below of ABC with side AC extended through D, mA  37 and
mBCD  117. Which side of ABC is the longest side? Justify your answer.
The plot of land illustrated in the accompanying diagram has a perimeter of 34 yards.
Find the length, in yards, of each side of the figure. Could these measures actually
represent the measures of the sides of a triangle? Explain your answer.
4
6
On the set of axes below, graph and label DEF with vertices at D( 4,4), E( 2,2),
and F(8,2). If G is the midpoint of EF and H is the midpoint of DF, state the
coordinates of G and H and label each point on your graph. Explain why GH DE.
5
7
In the spaces provided below, write the converse, the inverse, and the contrapositive of
the statement "If I run, then I am tired."
Converse:_________________________________________________________
_________________________________________________________________
Inverse:___________________________________________________________
_________________________________________________________________
Contrapositive:_____________________________________________________
Which conditional is logically equivalent to its original statement?
inverse
8
converse
contrapositive
Given: ABC and EDC, C is the midpoint of BD and AE
AB DE
Prove:
6