Question

Will fave and give medal, just check my answers please :)
Under the Euclidean theory.Determine the truth value of the FF.
F --a)Three points determine a plane.
T--b)Two intersecting lines determine a plane.
T--c)If line 1 is perpendicular to line 2 and line 2 is perpendicular to line 3, then line 1 is parallel to line 3.
T--d) If line 1 is parallel to line 2 and line 2 is parallel to line 3, then line 1 is parallel to line 3
...to be continued

Answer 1

F e) It is possible to have a triangle where all the interior angles are acute angles.
F f) It is possible to have a triangle where 2 of the interior angles are obtuse.
F g) It is possible to have a triangle with sides 1 cm, 2 cm, and 3 cm.
F h) If two triangles are similar, then the two triangles are congruent.

Answer 2

a is true
b is true
c true only if they lie in same plane
d true
e true
f true only in case of spherical triangle
g triangle of 0 height.
h may or may not be true.

Answer 3

a) is false if the three points all lie on a line(say on the x-axis)

Answer 4

yeah, a) is false for sure for the reason fwizbang stated.
b) is true, it's the intersecting part that makes it true.
c) in 2 dimensions this is true, in 3 or higher it's not. think of you're axis, they are all perpendicular to each other, but they uniquely point in different directions.
d) is true, if both 1 & 3 parallel to 2, then they are parallel to each other.
e) this is asking if 3 numbers less then 90 can equal 180. 180/3 = 60 so yes, a triangle can have 3 60 deg angles, or different combinations.
f) not in euclidean geometry, but in curved spaces, so answer is no.
g) a^2 + b^2 = c^2 , 1^2 + 2^2 = 3^2, 1 + 4 = 9, 5 = 9... hell no.
h) if they are similar, then one can be bigger or smaller version of the other, which doesn't necessarily mean equal (where congruent does mean equal), so no, this is false.

Answer 5

a.if three points do not lie in a line,then they definitely represent a plane.
g

Answer 6

h if two similar have corresponding sides equal ,then they are congruent