___sometimes, because if the points are collinear then there will be multiple planes that will go through that line see picture in postulate – 2.7 b. Points and are contained in exactly one line. E F ___always this is postulate 2.1_ – c. Two lines intersect in two distinct points and M N. ___never see postulate 2.6 – Exercises Determine whether each statement is or true. always, sometimes, never A line contains exactly one point. see postulate 2.3 A line contains exactly 2 points – Noncollinear points and are contained in exactly one plane. R, S, T Always see postulate 2.4 – Any two lines and intersect. m ℓ Sometimes, they could be parallel lines which would never intersect. If points and are contained in plane then is perpendicular to plane G H ℳ, ℳ. Never GH is in plane M. See postulate 2.5 – Planes and intersect in point T. ℛ Never the intersection of two planes is always a line. See 2.7 – 6. If points and are noncollinear, then segments , and are contained in exactly one plane. A, B, C , Always see Postulate 2.2 – In the figure, and are in and || . Q State the postulate that can be used to show each statement is true.
___sometimes, because if the points are collinear then there will be multiple planes that will go through that line – see picture in postulate 2.7 b. Points E and F are contained in exactly one line. ___always – this is postulate 2.1_ c. Two lines intersect in two distinct points M and N. ___never – see postulate 2.6 Exercises Determine whether each statement is always, sometimes, or never true. A line contains exactly one point. – see postulate 2.3 A line contains exactly 2 points Noncollinear points R, S, and T are contained in exactly one plane. Always – see postulate 2.4 Any two lines ℓ and m intersect. Sometimes, they could be parallel lines which would never intersect. If points G and H are contained in plane ℳ, then is perpendicular to plane ℳ. Never – GH is in plane M. See postulate 2.5 Planes ℛ and intersect in point T. Never – the intersection of two planes is always a line. See 2.7 6. If points A, B, and C are noncollinear, then segments , , and are contained in exactly one plane. Always – see Postulate 2.2 In the figure, and are in Q and || . State the postulate that can be used to show each statement is true.
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