POINTS, LINES AND PLANESBIG IDEA: REASONING AND PROOF

ESSENTIAL UNDERSTANDINGS:• Geometry is a mathematical system built on accepted

facts, basic terms, and definitions.• A postulate or axiom is an accepted statement of fact.

MATHEMATICAL PRACTICE:

Attend to precision

Getting Ready• Make the figure at the right with a pencil and a piece of

paper. Is the figure possible with a straight arrow and a solid board? Explain.

Undefined terms• In Geometry, some words such as point, line and plane are undefined.

Undefined terms are the basic ideas that you can use to build the definitions of all other figures in geometry. Although you cannot define undefined terms, it is important to have a general description of their meaning.

• A Point indicates a _______________ and has _______ size. You represent a point by a ________ and name it by a _________ letter.

• A Line is represented by a ______________ path that extends in two _______________ directions without ________ and has no _____________. A line contains ________________ many points. You represent a line by any _______ points or by a single _________ letter.

• A Plane is represented by a __________ surface that extends without __________ and has no _______________. A plane contains ______________ many points. You represent a plane by a _________ letter or at least ___________ points in the plane that do _______ lie on the same ___________.

Defined terms• Collinear points: points that lie on the __________ line

• Coplanar: points and lines that lie in the __________ plane

• Segment: part of a __________ that consists of two _____________ and all points ____________ them. You represent the segment by its __________ endpoints.

• Ray: part of a __________ that consists of ________ endpoint and all the points of the line on __________ side of the ____________. You represent the ray by its ____________ and another point with the order indicating the ray’s ____________.

• Opposite rays: two rays that ____________ the same ___________ and form a ___________. You represent the opposite rays by their _____________ endpoint and any other __________ on each ray.

EX: Name the parts of the diagram• a) Name 3 points that are coplanar.

• b) Name 3 points that are collinear.

• c) What are two other ways to name ?

• d) What are two ways to name the plane?

• e) What are two points that are not coplanar with points L, N and O?

• f) Name 3 rays in the figure.

• g) Which of the rays are opposite rays?

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Draw it• EX: Draw three collinear points , with .

Draw point . Draw line . Draw point between the endpoints of the line. Draw segment . Draw rays

• Name the following:• a) 3 non collinear points

• b) 2 rays which are not opposite rays

• c) 2 line segments that are on the same line

• d) the point of intersection of the lines

, and A B C between and B A C not on line D AC

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on the line E AD�������������� �

EC

and BD EB����������������������������

Postulate or Axiom: an accepted statement of fact

• Postulates, like undefined terms, are basic building blocks of the logical system in Geometry. You will use logical reasoning to prove general concepts in this book.

• Postulate 1-1: Through any two points there is exactly _______ line.

• Postulate 1-2: If two distinct lines intersect, then they intersect in exactly ________ point.

• Postulate 1-3: If two distinct planes intersect, then they intersect in exactly one __________.

• Postulate 1-4: Through any three non collinear points there is exactly one __________.

EX: Name the intersection of each pair of planes or lines in the figure.• a)

• b)

• c)

• d)

• e)

planes and ABP BCD

and RQ RO���������������������������������������� ���

planes and DCQADR

planes BCD and BCQ

and OP QP���������������������������������������� ���

Draw it• EX: Three lines that lie in the same plane, but two of the

lines do not intersect with each other and the third line intersects with each of the other lines in a point.

• EX: Two planes which do not intersect and a line which intersects each plane in a point.

1.2 P. 139 – 39X3, 14; 44 – 47, 48 – 66X3, 52, 53, 64; 73 – 75, 78, 80, 90 – 96 EVENS

35 questions