Theorems
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Transcript of Theorems
![Page 1: Theorems](https://reader036.fdocuments.in/reader036/viewer/2022082710/56812a98550346895d8e4cb6/html5/thumbnails/1.jpg)
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Parallel lines are like train tracks.They never cross.
![Page 3: Theorems](https://reader036.fdocuments.in/reader036/viewer/2022082710/56812a98550346895d8e4cb6/html5/thumbnails/3.jpg)
Parallel Line Theorems Two parallel lines on their own
are not vary interesting to us in terms of geometry.
But if straight line (called a transversal) intersects two parallel lines, then the angles created are very interesting to us…..
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These lines are parallel because they will never cross….
The dashed line is called a transversal, because it crosses both lines
![Page 5: Theorems](https://reader036.fdocuments.in/reader036/viewer/2022082710/56812a98550346895d8e4cb6/html5/thumbnails/5.jpg)
x
x
x
x
y
y
y
y
As soon as the transversal is drawn, a collection of angles are created.
These angles are equal because of OAT. Copy these to your sheet.
In this diagram, there is a collection of patterns that can be generated.
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y
y
“Z” pattern (alternate angles: AA)
![Page 7: Theorems](https://reader036.fdocuments.in/reader036/viewer/2022082710/56812a98550346895d8e4cb6/html5/thumbnails/7.jpg)
x
x
“Z” pattern
![Page 8: Theorems](https://reader036.fdocuments.in/reader036/viewer/2022082710/56812a98550346895d8e4cb6/html5/thumbnails/8.jpg)
x
x
y
y
“F” pattern (corresponding angles: CA)
![Page 9: Theorems](https://reader036.fdocuments.in/reader036/viewer/2022082710/56812a98550346895d8e4cb6/html5/thumbnails/9.jpg)
x
x
y
y
“F” pattern
![Page 10: Theorems](https://reader036.fdocuments.in/reader036/viewer/2022082710/56812a98550346895d8e4cb6/html5/thumbnails/10.jpg)
x
x
y
y
“C” pattern (supplementary angles: SA)
X + Y = 180O
( also called interior angles )
![Page 11: Theorems](https://reader036.fdocuments.in/reader036/viewer/2022082710/56812a98550346895d8e4cb6/html5/thumbnails/11.jpg)
Find X,Y and Z
70O
YX
Statement ReasonZ
Z = 70O OATY = 180O – 70O
= 110O
SA
X = 110O OAT
![Page 12: Theorems](https://reader036.fdocuments.in/reader036/viewer/2022082710/56812a98550346895d8e4cb6/html5/thumbnails/12.jpg)
HOMEWORK
see sheet