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MATH213_ALLSECTIONS_SPRING2011_0000_FINAL_EXAM.pdf
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MATH213 ALLSECTIONS SPRING2011 0000 FINAL EXAM.pd...
MATH213_ALLSECTIONS_SPRING2011_0000_FINAL_EXAM.pdfMath 213 Final Exam Spring 2011
MATH213 ALLSECTIONS SPRING2011 000...
MATH213_ALLSECTIONS_SPRING2011_0000_FINAL_EXAM.pdfMath 213 Final Exam Spring 2011
Page 4
6(12).
Complete the following proof with the appropriate steps and reasons.
Given:
ܥܣ
ത
ത
ത
ത
and
ܦܤ
ത
ത
ത
ത
bisect each other
at E
Prove:
ABCD is a parallelogram
Statement
Reason
1._______________________________
1. ________________________
2.
AE = EC, BE = DE
2.
________________________________________
3.
________________________________
3.
vertical angles are congruent
4.
ܤܧܥ∆ ؆ ܦܧܣ∆ ;ܦܧܥ ؆ ܤܧܣ∆
4._________________________________________
5.
൏ 5 ؆ ൏ 6; ൏ 7 ؆ ൏ 8
5. _________________________________________
6.
ܦܣ
ത
ത
ത
ത

ܥܤ
ത
ത
ത
ത
;
ܤܣ
ത
ത
ത
ത

ܦܥ
ത
ത
ത
ത
6. _________________________________________
7.
ABCD is a parallelogram
7.
________________________________________
7(6).
Sketch a Venn diagram showing the relationships among the following sets:
rhombuses, parallelograms,
squares, quadrilaterals.
Be sure to label each of your sets clearly.
A
B
C
D
4
1
2
3
5
6
7
8
E
Page 5
Name______________________________________
Instructor________________________________
8(5).
We are given that 1 lightsecond, the distance light will travel in one second, is approximately 300,000
km, and that the distance from the Sun to the Earth is on average 150,000,000 km.
How many light
minutes
(the distance light travels in one
minute
) is the Sun from the Earth? (Round to the nearest tenth).
9(8).
Consider a square with a perimeter of 48 inches.
What is the area of the largest circle that can fit inside
the square?
Show all work.
Include appropriate units on your final answer.
10(4).
Using the centimeter grid below draw a parallelogram that is not a rectangle that has an area of 32 square
cm.
Label the appropriate dimensions.
Page 6
11(8).
Consider the figure at
right.
a.
Name a pair of similar
figures.
b.
Find the lengths of segments
ܦܣ
ത
ത
ത
ത
,
ܦܤ
ത
ത
ത
ത
, and
ܧܦ
ത
ത
ത
ത
.
Show work.
12(10).
You are building a tree house that is shaped like a cube 6 feet on each side with a squarebased pyramid
on top for the roof.
The height of the tree house is 10 feet from the center of the floor to the peak of the roof.
You have a window on each wall side of the cube that is 2 feet by 2 feet.
You want to paint your tree house red (as a matter of Terrapin pride).
What is the total exterior surface area of
the tree house?
(Do not include the windows, but do include the roof and the bottom.)
Show all work.
Include
appropriate units on your final answer.
Page 7
Name______________________________________
Instructor________________________________
13(10).
A bag of popcorn can be approximated as a hexagonal prism with the dimensions shown below.
(Hint:
The hexagonal face can be divided into two congruent trapezoids by a horizontal line through the center)
a.
Find its volume in cubic inches.
b.
How many cubic cm is this?
Use the conversion 1 inch = 2.54 cm.
Round your final answer to the nearest
whole number.
4 in
3 in (top to
bottom of
hexagon)
5 in
8 in
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