hw #9-8
pg 367 self-test 2
Chapter Review and Test on pgs 369-371 #1-infinity will make for much fun & rejoicing.
Industrious and forward thinking folks would take the time to plunk the chapter summary into their G.B.'s... Other industrious but less organized folks might start looking for their G.B.
OK, Theorem 9-12... we were on the right track...
ReplyDeleteTake a look at Classroom Ex#7 on pg 364...
We draw the chords connecting AD and BC
That creates trngl-PBC and trngl-PDA
Angl-A cngrnt Angl-C cuz both cut arc-BD
So trngl-PBC ~ trngl-PDA cuz of AA~
Corr sides in proportion and props of proportions take care of the rest, yes?
OK, Theorem 9-13...
ReplyDeleteSee pg 365#10...
Draw chords AC & BC
Angl-PCB (tangent & a chord) and Angl-PAC (inscribed angle) both cut the same arc and are congruent since both situations (tangent & a chord AND inscribed angle) mean that the measure of the given angle is half the measure of the intercepted arc. (yes?)
That does it... since Angl-P is in both triangles...
Trngl-PCB ~ Trngl-PAC cuz of AA~
Corr sides and props of props complete the proof.
For #19
ReplyDeleteLet PA=x
So. PB=x-11
ok?
So x(x-11)=12(5)
So... quadratics, baby.. to solve them we have to set them equal to zero and use the ZERO PRODUCT PROPERTY...
x^2-11x-60=0
NOW, you have a choice:
Factoring (FUN & EASY, remember?)
or QUADRATIC FORMULA... why did we memorize this??
a=1, b=-11, c=-60
I prefer factoring... can you find two number that multiply to -60 and sum to -11??
-15 and 4, right?
So,
(x+4)(x-15)=0
Solution x={-4, 15}
Since x represents the length of PA, the negative solution is EXTRANEOUS and cannot be used... so PA=15
Given that AB=11,
PB=PA - AB
PB=15-11
PB=4
Too easy, huh?
yeah thanks mister c!
ReplyDeleteMr. C remember I am meeting with u on Monday
ReplyDeleteSee u in the morning!
ReplyDelete