geomentry unit 4 Flashcards
1
Q
image
A
tranformed figure
2
Q
preimage
A
original figure
3
Q
rigid motion
A
translation, rotation, reflection. Does not change shape or size
4
Q
r 90cc
A
x,y
-y,x
5
Q
r90c
A
x,y
y,-x
6
Q
r180
A
x,y
-x,-y
7
Q
ref line y=x
A
x,y
y,x
8
Q
ref line y=-x
A
x,y
-y,-x
9
Q
r 270 cc
A
x,y
y,-x
10
Q
reflectianl symmentry
A
line of symenty , when relfected stays same
11
Q
ratational symentry
A
when roatated certain amout of times looks same, point of symmentry, 2 fold, 3 fold, etc
12
Q
euclidean geomentry
A
based on 5 postulates created my euclid listed below :
- a striaght line segemnt can be drawn between any 2 points
- any straight line segemtn can be exteded indefinitely
- a cricle can be drawn with any certer and radius
- all right angles are equal to one another
13
Q
playfair axiom
A
created my jon playfoiar as th3 5th postulate too long
- through a given point, not on a given line, there is excatly one line parallel to the given line
- alos known as parallel postulate
14
Q
non- euclidean geomentry
A
created by Lobachevsky and Riemann
15
Q
spherical geomentry
A
- created by riemann
- created chapge to playfailr axim
- riemann’s neagation : through a given point not ona given line there is no line paralle to the given line
- geomenty pictured on a sphere
- lines called great circles
16
Q
Hyperbolic geomenty
A
- created by Lobachevsky
- made chage to pplayfair’s axiom
- Lobachevsky’s negation : Through a given point not on a given line there is more then one line parallel t the given line.
17
Q
euclidean geo fact
A
- sum of triangle 180
- line can be exedn infinatley
18
Q
spherical geo fact
A
- sum of triangle greater an then 180
- line can not be extended infintly, because it returns to where it starts
19
Q
hyperbolic geo fact
A
- sum of angle sin triangle lesss than 180
- a line may or may not be extended infinitrly
