In geometry, what’s the difference between a postulate and a theorem? give an example of each

Step-by-step explanation:

This is a course specific question. What I think is a postulate may not be listed in your lesson. A postulate is a statement that is assumed to be true. There has not been an exception found in over 2000 years. A postulate does not require proof: its truth is accepted.

Example: Two points on the same plane have exactly 1 line that can go through them.

Theorem: using the postulates to begin with, a theorem is a statement that can (and should) be proved.

Example: Two lines that are on the same plane, if they intersect at all, intersect only once.

a^2 + b^2 = c^2

This well known theorem can be proved well over 100 ways.

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)

by definition, an arc subtended by a central angle of some given measure has the same measure. so .