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MATH 131 MIDTERM EXAM
FUN KNEUBAUER
NOVEMBER 2, 2006
' 100 POINTS YOUR NAME:
CIRCLE YOUR SECTION: MWF TTH MAKE IT CLEAR WHAT YOUR FINAL ANSWERS ARE AND MAKE SURE CAN CLEARLY READ YOUR WORK. USE SCRAP PAPER IF
NECESSARY. Number 1 (12 points); Draw all possible patterns that will fold up into an open
top cube (a cubical box with the top lid missing). Remember, for a pattern, a piece
of the cube should be joined to another piece along a whole edge, not just a corner.
For two patterns to be cOnsidered different, you should not be able to match the
patterns up when they are cutout. You don't need to carefully construct each
pattern, just free—hand draw them; N o explanation required, just draw the pictures. :9 ‘1 x
K Number 2 Part (i) (12 points): Find formulas involving 11 for the following, and
eXplain how you got each formula. The number of faces on a prism with an n—gon base. The number of vertices of a prism with an n—gon base. The number of edges of a prism with an ngon base. Number 2 Part (ii) (4 points): Verify that Euler's formula holds for a prism with
an ngon base. “(Q kl): Number 3 (12 points): For this question refer to the designs below. Note that the
regions of different colors must be considered different in determining the
symmetry properties. Answer the following questions, no explanation required. Which design has only'reﬂectional symmetry? Which two designs have Only rotational symmetry? Which design has both rotational and reﬂectional symmetry? Number 4 (8 points): In the figure below, ABCD and EFGH are squares. Fill in
the blanks, no explanation required. The 90 degree clockwise rotation through point 0 sends Point A to
Point H to
Line segment CG to
Line segment BE to 3 Number 5 (12 points): The year is 3256 and you are on the planet Gibberish
studying the culture of the native inhabitants, the Gibberites. You are studying 7 their system of geometry and learning about a class of shapes that they call
frumpiters. Listed below are ﬁve of their deﬁnitions and one theorem. Using this
information draw a Venn diagram that accurately shows the relationships between
the five types of frumpiters. No explanation required, just draw the picture. Definition 1: A zerbert is a frumpiter for which six sides are qwerty. Definition 2: A henorb is a frumpiter with five jork angles. Definition 3: A somorg is a frumpiter whose sides all have the same
length. Definition 4: A kipford is a fumpiter for which at least three sides are
qwerty. Definition 5: A vibort is a frumpiter with ﬁve jork angles whose sides all
have the same length. Theorem: A11 henorbs and somorgs are zerberts. Number 6 Part (i) (8 points): Use a compass and a straightedge to bisect the
angle below. Number 6 Part (ii) (10 points): Using a congruence theorem and any relevant
definitions prove that your construction in Part (i) actually does bisect the given
angle. Label your picture above so that you can refer to it in your explanation. Number 7 (12 points): In the figure below line p is parallel to line q. Also, line r
is parallel to line s. Without using a protractor calculate the values of the angles W, X, Y, and Z. Brieﬂy e lain your reasoning for each and show any relevant
calculations. {2
“L G3” Angle W: Angle X: Angle Y: Angle Z: 1%,?) Number 8 (10 points): In the figure below line segment EF is parallel to line
segment BC. Find the length of the line segments FC and BC. Round your answer
to two decimal places. Brieﬂy explain your method and show your work. ' Line segment FC ‘ Line segment BC ...
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