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1-1 Points, Lines and Planes

Learn about points, lines, and planes in geometry. Understand the definitions, properties, and intersections of these fundamental concepts.

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1-1 Points, Lines and Planes

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  1. 1-1Points, Lines and Planes Undefined Terms point – a location; noshape or size Name the points in the figure provided: Answer: pt. A, pt. B, pt. C, pt. D line – made up of points; has nothickness or width; extends infinitely in twodirections Name the line in the figure provided: Answer: line l , AB, AC, BC, BA, CA, or CB plane – flat surface made up of points extending infinitely in alldirections Name the plane in the figure provided: Answer: plane N, plane ABD, plane ACD, plane BCD

  2. 1-1Points, Lines and Planes Undefined Terms point – a location; noshape or size Name the points in the figure provided: Answer: pt. A, pt. B, pt. C, pt. D line – made up of points; has nothickness or width; extends infinitely in twodirections Name the line in the figure provided: Answer: line l , AB, AC, BC, BA, CA, or CB plane – flat surface made up of points extending infinitely in alldirections Name the plane in the figure provided: Answer: plane N, plane ABD, plane ACD, plane BCD

  3. 1-1Points, Lines and Planes Undefined Terms point – a location; noshape or size Name the points in the figure provided: Answer: pt. A, pt. B, pt. C, pt. D line – made up of points; has nothickness or width; extends infinitely in twodirections Name the line in the figure provided: Answer: plane – flat surface made up of points extending infinitely in alldirections line l , AB, AC, BC, BA, CA, or CB Name the plane in the figure provided: plane N, plane ABD, plane ACD, or plane BCD Answer:

  4. 1-1Points, Lines and Planes collinear – on the samelineopposite: noncollinear coplanar – in the sameplaneopposite: noncoplanar Name 3 collinear points: Answer: pt. R, pt. T, pt. Q or pt. P, pt. T, pt. N Are points P, T, and Q collinear? Answer: no (not on the same line) Are points P, T, and Q coplanar? Answer: yes; all in plane S

  5. 1-1Points, Lines and Planes intersection – set of points that 2 or more geometric figures have incommon (where they cross) Find the intersection of plane Nand AE. Find the intersection of BC and CD. Answer: pt. B Answer: pt. C point Two lines intersect in a ________.

  6. 1-1Points, Lines and Planes Find the intersection of plane MXR and plane MNP. Answer: MN or NM Find the intersection of plane NRQ and plane WTQ. Answer: PQ or QP line Two planes intersect in a ________. space – a boundless, three-dimensional set of all points

  7. 1-2Linear Measure line segment (segment) – a measurable part of a line between twoendpoints Name the line segment: RS or SR AB  BC, MP  MN Answer: congruent segments – segments that have the samemeasure Examples:

  8. 1-2Linear Measure Betweenness of Points Point M is between points P and Q if and only if P, Q, and M are collinear and PM + MQ = PQ Find EF. Solution: EF = ED + DF EF = 1.2 + 1.9 EF = 3.1 cm

  9. 1-2Linear Measure Betweenness of Points Find the length of GH. Solution: FG + GH = FH GH = FH – FG GH= 15 – 9.7 GH = 5.3 mm

  10. 1-2Linear Measure Betweenness of Points Y is between C and D. If CY = 2.3, YD = 3x, and CD = 9.8, find YD. 3x 2.3 Solution: CY + YD = CD C Y D 2.3 + 3x = 9.8 9.8 – 2.3 – 2.3 3x = 7.5 YD = 3x 3 3 YD = 3(2.5) x = 2.5 YD = 7.5

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