geomentry unit 4

Question 1

image

Answer 1

tranformed figure

Question 2

preimage

Answer 2

original figure

Question 3

rigid motion

Answer 3

translation, rotation, reflection. Does not change shape or size

Question 4

r 90cc

Answer 4

x,y
-y,x

Question 5

r90c

Answer 5

x,y
y,-x

Question 6

r180

Answer 6

x,y
-x,-y

Question 7

ref line y=x

Answer 7

x,y
y,x

Question 8

ref line y=-x

Answer 8

x,y
-y,-x

Question 9

r 270 cc

Answer 9

x,y
y,-x

Question 10

reflectianl symmentry

Answer 10

line of symenty , when relfected stays same

Question 11

ratational symentry

Answer 11

when roatated certain amout of times looks same, point of symmentry, 2 fold, 3 fold, etc

Question 12

euclidean geomentry

Answer 12

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

Question 13

playfair axiom

Answer 13

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

Question 14

non- euclidean geomentry

Answer 14

created by Lobachevsky and Riemann

Question 15

spherical geomentry

Answer 15

• 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

Question 16

Hyperbolic geomenty

Answer 16

• 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.

Question 17

euclidean geo fact

Answer 17

• sum of triangle 180
• line can be exedn infinatley

Question 18

spherical geo fact

Answer 18

• sum of triangle greater an then 180
• line can not be extended infintly, because it returns to where it starts

Question 19

hyperbolic geo fact

Answer 19

• sum of angle sin triangle lesss than 180
• a line may or may not be extended infinitrly