To our geometry teacher that has taught us all year long THANK YOU Mrs. Dinger!!!!!
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Table of contents
pages
Chapter 1 Probability and Statistics 6
a. Calculate Probability 10
b. Probability of Independent 11
c. Probability of compound events 14
d. Recognize and explain in everyday situation 14-17
Chapter 2 Transformations 18
a. Reflection 19-20
b. Translations 19-21
c. Rotations 19
d. Slope Criteria or parallel and perpendicular lines 19
Chapter 3 Angle Pair Relations 24
a. corresponding angles 25-27
b. alternate interior angle 25-27
c. alternate exterior angle 25-27
d. consecutive interior angle 25-27
pages
Chapter 4 Congruent Triangles 28
a. Distance formula 30
b. Pythagorean Theorem 30
c. ASA Theorem 31
d. SSS Theorem 32
e. SAS Theorem 33
Chapter 5 Singular Triangles and Trigonometry 34
a. AA Similarity Postulate 35
b. Special Right Triangles 36
c. SOH-CAH-TOA 37-40
d. Indirect Measurement Methods 43-44
e. Dilation 45
Chapter 6 Polygons 46
a. Rectangles 49
b. Triangles 49
c. Your choice 1 50-53
d. Your choice 2 54
pages
Chapter 7 3-D Geometry 55
a. Solids 56
b. Volume of Prisms/ Pyramids 57
c. Surface Area/ Nets 58-60
d. Cavalier's Principle 61
Chapter 8 Circles 62
a. Similar Circles 62
b. Center of Rotations 63
c. Center of Dilations 64
d. Angles Formed In Circles 65
I'm Tammy and I thinkGeometry is Life
My adventures........
Chapter 1Probability and Statistics
In 2012 Tammy went to the summer olympics and in 2014 went to
the Winter olympics. She really excited
to attend the Olympics.
I love the Olympics!
Two years later, as she got older, she wondered differentprobabilities of what could have happened at the 2012 summer
olympics and the 2014 winter olympics. After Tammy was
going to find different probabilities of her marbles.
independent events~ one event has no effect in another event P(AnB)= P(A) P(B)dependent events~ one event has an
effect on another event P(AnB) =
P(B) P(B/A)/..What are events?
2.P(USA are female)72.5/132=.551.p(U.S.A won gold)=55/132=.423.P(USA won gold and are female)33.5/132=.254.P(USA won gold/female)=33.5/72.5=.255.P(female/USA won gold)=33.5/72.5=.616.(male/USA) won gold)=21.5/55=.39
Olympics notesmy marblesIdentifying dependent and independent events$0.35 to playIf you get 2 green marbles you win $1p( 1st green)=3-5p(1st green n 2nd green)=P(1st green).P(2nd green / 1st green)
givendependent on 1st pick
3-5.2-43-5.1-23-=10=.30.30.$1=0.30you pay $0.3530% chancewithout replacing marbles
Later that day Molly went to Tammy's housebecause she needed help on her homework.
I need Tammy!
I can't do my homework because I don't know what a compound event is.
A Compound event is 2 or moreevents at the same time.Lets go inside
and i'll help you.
Molly's Homework
Okay sounds great!
I will show you a my own demonstrationon compound events by using my marbles!
After we could jump rope outside.
So Molly, I have a bag of twelve marbles and there are four blue marbles and two black marbles and
the rest are white.We want to find the probability of
choosing a blue marble and then a black marble.
But Tammy how do we start?
Step 1:We must find the probability of each
individual event.
There are four blue marbles outof the twelve marbles in the bag.
There are two black marbles outof the twelve marbles in the bag.
Ohh so the probability of choosing a blue marble and then a black marble is 1/18.
Now I could do my homework when
I get home, thank you so much Tammy.
Then Step 2: We must multiply theprobabilities of each individual event.
...21...22...23 Keep going Molly get 25.
Then Tammy and Molly went outside to play. 
Chapter 2Transformations
Then one day Tammy decided to go to the lake
to swim for a little while. While she was there
she noticed many frogs leaping and jumping
around. She was so curious that she tried to figure
out the reflections, translations, and the rotations of
the leaping frogs. So she watched the
transformations of the frogs and she made a graph
that related to them.
2418681012141620222426283032
image 1
5101520253035
image 2image 3image 4image 5
Hmmmmm..........
6
7
180oTammy already knows what reflectionsand translations are.
.... Reflection-Reflection is any type a shape is moved from its
original coordinates on its coordinate plane
-Reflect across x-axis:Make y values negative
-Reflect across u-axis:Makes values negative
...
...Translations-Subtract from x-values when moving left
-Add to x-values when moving right
-Subtract from y-values when moving down
-Add to y-values when moving up ...
.....
Image 1
Pre-Image
Final Image
DescriptionImage 2Translation (x+6,y+7)Image 2Image 3Rotation 180 degreesImage 1Image 3Image 2Image 5Image 4Image 4Rotation 90 degreesRotation 90 degrees counter-clockwise
translation
I'll see you soon frogs.
Angle Pair Relations
I love this book!
The next day she remembered she had homework for her teacher Mrs.Dinger.
Her homework was to research about
Angle Pair Relations and do some problemsChapter 3angle pair relations
alternative interior angles
(zig zag/ s-shape)alternative exterior
angles
[v- shape (not touch)]consecutive interior
angles
c-shape = 180corresponding
angles
f- shape
Mrs.Dinger's homework assignment it's to
connect the angle pair relations with the right
word for each of the angle pairs in the work
sheet assign.
word bank
- corresponding angle
- alternate interior angle
- alternate exterior angle
- consecutive interior angle
Name: Tammy FlutterbutterTeacher Mrs. Dinger
alternate exterior angleCorresponding angleconsecutive interior
anglealternate interior
angle
The following day Tammy went to go to a
field trip to a forest named "Sky watching"
that was located in a forest named Sky
Forest. It was named Geo because the
students can compare the stars with a
geometric theorem.
Mrs. Dinger assign number on the triangles lines for the students can do math
problems using the theorems below.82816
Wow the three stars created a triangle
To start the work sheet start solving the distance
from the stars.
534Pythagorean Theorema^2 + b^2 = c^23^2 + 4^2 = 5^29 + 16 = 2525 = 25Distance Formula
(5-1)2+(2-5)2D =D =(4)D =D =D =2+(-3)216 + 9525
ASA TheoremGiven: M is themidpoint of AD and BCProve: AB CD1. Given: M is the midpoint of AD and BC6. AB CD2. AM MD
BM MC5. angle A angle D3. angle AMB angle DMC4. angle ABM angle DMC____________________________________=====~~~~~
A2GDBH4=F__J3_=ABDE6ECFD_3=12Ratios of sides lengths of angles ABC and angles DEF ____28CAShortest sides=_EFBCRemaining sidesLongest sides__=__6923=Ratios of sides lengths of angles ABC and angles GHJRemaining sidesShortest sidesAB___Longest sides6GH6=1CA=7__12=146__=JG___HJBC=__129106966141048SSS Similarity TheoremSAS Similarity Theorem Use the SAS Similarity Theorem is to find the ratio of the corresponding sides.
15__SR=1254SP_____4 + 12SP + PRSP_______=4=4416=__ST_______SQ + QT__SQ==5 + 15SQ5=_____4=__520
Mrs. Dinger'sThe next day in Tammy's Geometry class Mrs.Dinger was going to teacha new lesson. The new lesson was going to be about Similar Triangles and
Trigonometry.
Chapter 5Similar Triangles and Trigonometry
Similar Triangles and Trigonometrya.AA Similarity Postulate
b.Special right trianglesSimilar Triangles and Trigonometry
These are of special right triangles children.
Soh-Cah-ToaSine=opposite/hypotenuse Cosine=adjacent/hypotenuse Tan=opposite/adjacentSineCosineTangentSimilar Triangles and TrigonometryC.Then Mrs.Dinger made some problems on the board for the students to solve. She gave the students some time to solvethe problems and afterwards she would call on some people to demonstrate their answers on the board.Mrs.Dinger chose Jimmy to do number one, Sally to do number two and she asked Tammy to do
number three.
opp1.2.
12 cm213.x
sin=3/6Find sin
So first I found out that I could find sin by using SOH. I remembered that SOH was opposite over hypotenuse.
I saw that the opposite side was 3 and the hypotenuse I
knew that the hypotenuse was right because it was
the longest side.Then I substituted the numbers given and
sine=3/6.
My final answer is x=4.3Mrs. Dinger.-First Sally used sin as she figured
the numbers given
-Then she substituted the numbers
given into the sine equation
My result isx=16.
Then Mrs.Dinger told the students to go outside and measure the flag pole and also the length of their shadow
towards the pole.
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