Page 33


Problem 1


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Problem 2


Two proofs that the angles in a quadrilateral sum to 360 degrees are found in the pictures below. You should be certain that you understand BOTH proofs. Then you should answer the remaining questions, which have answers 540, 720, and 9900 respectively.

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Problem 3


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Problem 4


n=33, w=108, u=26



Problem 5


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Problem 6


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Problem 7


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Problem 8


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Problem 9


(a) If point P is on the line y=x, then point P is equidistant from the coordinate axes.

QUESTION: Are both the statement and its converse true? Not true? Can't determine?

(b) If x=1, then x^2=1

Converse: If x^2=1, then x=1

(c) If x=1, then x^3=1.

Converse: If x^3=1, then x=1.



Problem 10


Converse: If a quadrilateral has both pairs of opposite angles congruent, then the quadrilateral is a parallelogram.

This is TRUE!

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Problem 11


Look back at problem 7 above. Then try to find other ways to do it.




Page 34


Problem 1


page 34 problem 1
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Problem 2


page 34 problem 2
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Problem 3


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Problem 4


If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

This is true.

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Problem 5




Problem 6


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Problem 7


Some basic angle chasing...

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Problem 8


First off, you must calculate the length. If you have done that correctly, the length is



Next, find any other vector such that the dot product with it and [6,2,3] is zero. I choose the vector [3,0,-6]. To make it the same length as the given vector, I divide by its length, and multiply by 7.



Now, multiply by 7.





Problem 9


Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)



Problem 10


Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)



Problem 11 and 12


Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)



Problem 13




Problem 14


to be discussed in class.



Problem 15


Well? In what sense is a transformation a function??