Page 31


Problem 1


(a) BPQ and PQC

(b) MPA and DQT

(c) CQT and APQ, TQD and QPB



Problem 2


Just do it. If you do it correctly, the lines will have the same slope, and hence, be parallel.



Problem 3


Parallel in both cases.



Problem 4


In each case, the pairs are equal, with the exception of (d), in which they are supplementary.



Problem 5


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 6


They must be equal.



Problem 7


Convince yourself that triangle ADP is isosceles. Convince yourself that angle ADP is 150 degrees. Convince yourself that the angles DPA and DAP are both 15 degrees.

page_31_problem_7.png



Problem 8


Dot Product? am + bn + cp = 0.

However, let's use the distance formula and see if we arrive at the same result.

2010-11-28_1422.png

And, it does!



Problem 9


am+bn+cp=0



Problem 10


am+bn=0




Page 32


Problem 1


There are a whole slew of vectors that will work. In fact, and vector [x,y,z] that satisfies 5x+7y+4z=0 will work. Hence, [4,0,-5] is one and [0,-4,7] is another.



Problem 2


page 32 problem 2
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Problem 3


Angle TAC is equal to the sum of the two interior angles on the other side of the triangle (these are called remote interior angles). You should prove this.



Problem 4


page 32 problem 4
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Problem 5


They add up to 360 degrees, but I will wait for your proof.



Problem 6


n=36, x=98, y=73

I will wait for your work on this.



Problem 7


In each case, the angle is 107 degrees. Why?



Problem 8


The angles add up to 360 degrees. The opposite angles have equal measures. Adjacent angles are supplementary.

I will wait patiently for your proofs of these three facts.



Problem 9


vector.png





Problem 10


Here is my first attempt at using my new portable document camera.

2010-11-30_0002.jpg

11-30-2010_Image001.jpg






be sure the double the .717 because that is only the time it takes to go halfway. You should get about 1.4 hours