FBQS
Page-9.9
Question 1:
Two distinct points in a plane determine a ________ line.
Answer 1:
Axiom 5.1 states that 'Given two distinct points, there is a unique line that passes through them.'
Two distinct points in a plane determine a __unique__ line.
Question 2:
Two distinct __________ in a plane cannot have more than one point in common.
Answer 2:
Let p and q be two distinct lines. Suppose these two lines intersect in two distinct point say A and B. So, there are two lines passing through two distinct points A and B. But, this contradicts the axiom that only one line can pass through two distinct points. Hence, our assumption that two lines intersect in two distinct points is wrong. Thus, two distinct lines cannot have more than one point in common.
Two distinct __lines__ in a plane cannot have more than one point in common.
Question 3:
Given a line and a point, not on the line, there is one and only __________ line which passes through the given point and is ___________ to the given line.
Answer 3:
The equivalent version of Euclid's fifth postulate (Playfair's Axiom) states that 'For every line l and for every point P not lying on l, there exists a unique line m passing through P and parallel to l.'
Given a line and a point, not on the line, there is one and only __one__ line which passes through the given point and is __parallel__ to the given line.
Question 4:
A line separates a plane into _______ parts namely the _______ and the _______ itself.
Answer 4:
A line divides the plane into two regions. These two regions are two half planes.
Plane separation postulate states that every line divides any plane containing the line into three non-overlapping regions i.e. the line and the two half planes.
A line separates a plane into __three__ parts namely the __two half planes__ and the __line__ itself.
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