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table of contents

ch.1: Probability and Statistics

              "the coin toss"

              "independent and dependent events"

              "prob. of compound events"

ch.2: Translations

         "Ben and Greg's adventures"

         "ben and greg find a fly"

         "stranded"

ch.3: Angle pair relations 

         "finding the right angles"

ch.4: Distance formula/Pythagorean theorem

         "the rat smells cheese"

ch.5: "How to Use SohCahToa to Find the Trig       

           Functions of a Right Triangle"

ch.6: Painting a House

          "alexis is barn"

ch.7: 3-D Geometry

         cavalieris principle

        "a question in shapes ville."

ch.8: Circles

         "Saturns dilemma"

Today is race day! Guy and Ding have

worked all summer to build the fastest, most 

aerodynamic race car.

BUT WAIT! who's going to drive it.

Guy and Ding agree on a coin toss, winner gets to 

race.

what is the probability that ding will win 

the coin toss?

well, first you have to determine the 

probability that two people will win one coin 

toss.

ding and guy both want to win.

second, determine how many times they 

toss the coin. which is once.

so if,

ding is one person    &    guy is one person 

and picks tales               and picks heads

they both have a 50% chance out of 100, that 

one of them will win the coin toss and get to 

race.

"independent & dependent events"

cars 1,2 and, 3 each have Goodyear brand 

tires. they were all manufactured on the same 

day. same shape, same size, each tire installed 

the same way. 

what is the probability that tires on car 2 will 

go flat? what type of event is it?

                         1

     3        2      

okay so,

first determine if its dependent or independent.

this is a dependent event."HOW DO I KNOW?"

1. all cars have the same tire brand manufactured 

and installed the same day.

2.each tire was installed the same way.

3.they all have the same start time.

          so, for the tires to go flat and be destroyed        

          would be a total suprise because no one     

          would have guessed. 

          so, car 2 would have a 33% out of 100 

          chance that its tires will be destroyed.as 

          do tires 1 and 3.          

okay, what is the probability that car #3 will 

slow down first because the engineer didn't fill 

the gas tank with the correct amount of gas?

     well, you see it would be a 100% chance.

     this is a dependent event the engineer did           

     not make the correct measurements. which 

will eventually lead to the car slowing down 

near the end of the race.

"BEN AND GREG'S ADVENTURE"

One day a frog named ben and his best friend greg 

were sitting looking and enjoying the pond.

Ben tells greg: i enjoy watching 

the reflections in the pond. i 

wonder how they got there.

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"well." says greg, "think of the pond as a       

 mirror."

 "pretend that your standing on a grid, and the line 

between you and the pond is the X-axis"

l    l    l    l    l    l    l    l    l   

l    l    l    l    l    l    l    l    l

l    l    l    l    l    l    l    l    l

l    l    l    l    l    l    l    l    l

l    l    l    l    l    l    l    l    l

l    l    l    l    l    l    l    l    l

l    l    l    l    l    l    l    l    l

l    l    l    l    l    l    l    l    l

so, every point in 

your side of the grid 

is going to mirror on 

to the other side of 

the grid.

for example: your 

eyeball is located

 (-4,-1)   so on the 

mirror your eyeball 

will be located (-4,1)

"BEN AND GREG FIND A FLY"

"okay greg lets get him!"

                "oh no! hes stuck on that         

                 giant oddly shaped       

                 spiderweb. how   

                 are we gonna get him?" 

"we are going to translate ourselves."

                   "how does that bring us to him?"

"since he is on point 

(-3,-3) and we are on 

point (3,3), we are 

going to translate down 

6 points and left -5 

points."

 "And for sure we got 

him"

"STRANDED"

ben and greg went for a ride on a leaf an got stuck 

in the middle of the pond with only a rope and a 

paddle.

"i know how to get back!" shouts greg.

"we can rotate ourselves back with this rope 

that paddle and one of those plants."

"show me how" says ben whose eager to get 

home.

"okay so we need to pick a plant who will put 

us in the correct length of rotation. 

once we do that you can use your laso skills to 

bring us home." 

so your going to laso the first plant, which will 

stand as the center of our graph. 

once you do that i will paddle our way back to 

land. we should rotate in a full circle, to land.

we made it using rotations.

"finding the right angles"

    1.corresponding 

       angles

    2.alternate interior

       angles

    3.alternate exterior 

       angles

    4.consecutive 

       interior angles

we need to find 

angles that match 

the ones on the list

this would be a good example for corresponding 

angles because it has to 90 degree angle and they 

are right next to each other.

to help remember them they make a F shape.

this would be an alternate interior angle because the 

angles are on both sides and different corners.

the best way to recognize them would be to look for 

a Z shape.

these are alternate exterior angles because 

they have the same angles but on the exterior 

instead if the inside.

they don't touch

consecutive interior angles because there is 

consecutive angles in one part, both the same.

 C shape, always 180 degrees

  1.corresponding 

     angles.

  2.alternate interior

     angles.

  3.alternate exterior

     angles.

  4.consecutive interior

     angles.

YEAH! 

we finished. we 

identified all of them

"the rat smells cheese"

gale the rat was hungry. luckily for her she 

smelled cheese no that far from her. but wait the 

cheese was on the beautiful white tile floor and 

the cat not lurking far from it. 

gale is going to have to find out how far she is 

from the cat so she has a safe distance to run.

gale is at point (-2,1) and the cheese is at point 

(1,5). now we have to find out how far apart they 

are.

gale is going to have to use the distance formula to 

figure this one out.

you can draw in the 

lines.

now gale has to 

subtract the x-values 

and the y-values.

5-1=4

1-(-2)=3

then shes going to use 

the PYTHAGOREAN 

THEOREM to find the 

length of the third side.

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