05/03/23 1.1: The Building Blocks of Geometry

1.1: The Building Blocks of Geometry

Expectation:G1.1.6:Recognize Euclidean geometry as an axiom

system. Know the key axioms and understand the meaning of and distinguish between undefined terms (e.g., point, line, and plane), axioms, definitions, and theorems.

05/03/23 1.1: The Building Blocks of Geometry

Undefined Terms

1.

2.

3.

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Points

Models of points

0 dimensional (have no size)

-Dots-Stars in the sky-Cities on a map

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PointsNaming points

- Use capital letters

A

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LinesPerfectly straight extending infinitely without thickness.

Models of Lines- roads- hallway- edge of a box

1 dimensional

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Naming Lines

l

Line l

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Naming Lines

A

B

Line AB or BA

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PlanesInfinite, flat surface without thickness.2 dimensional

Models of Planes-desktop-wall

-rooftop

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Drawing Planes

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Naming Planes

Plane R

R

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Naming Planes

Plane PQR, PRQ, RPQ, RQP, QRP or QPR

PR

Q

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Collinear Points Defn:Three or more points are collinear iff they are on the same line.

A B C

A, B and C are collinear.

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Coplanar Points

Defn: Four or more points are coplanar iff they are on the same plane.

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Coplanar Points

P, Q, R and S are coplanar points.

PR

Q S

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SegmentsDefn: A segment is a part of a line that begins at one point and ends at another. The points are called the endpoints of the segment.

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Segments

A B

AB

This is not a segment!!!

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Segments

A B

The segment with endpoints A and B: denoted AB or BA

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RaysDefn: A ray is a part of a line that starts at a point and extends infinitely in one direction. The point is called the endpoint of the ray.

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Rays

Y

Z

The ray with endpoint Y containing Z: denoted YZ (may not be denoted ZY or ZY).

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AnglesDefn: An angle is a figure formed by two rays with a common endpoint. The common endpoint is called the vertex of the angle and the two rays are called the sides of the angle.

05/03/23 1.1: The Building Blocks of Geometry

Angles

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Angles

vertex of the angle

sides of the angle

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Naming an AngleThere are 3 ways to name an

angle: ( represents an angle)1. The vertex.2. A point from each side and

the vertex (vertex is between the other points).

3. A number.

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Naming Angles

A

B

C

1

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Naming Angles

A

B

C

B

1

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Naming Angles

A

B

C

ABC or CBA

1

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Naming Angles

A

B

C

1

1

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Intersect and Intersections

If 2 figures share one or more points, then they intersect. The point or points they have in common is called their intersection.

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Postulates

A postulate is a statement that is accepted as being true without proof.

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Complete Activity 1.1 on page 12.

You may work in pairs.

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Intersecting Lines Postulate

If two lines intersect, then their intersection is a point.

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Intersecting Planes Postulate

If two planes intersect, then their intersection is a line.

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Unique Line PostulateThrough any two distinct points,

there is a unique (one and only one) line.

Sometimes this is stated in an alternate form: ”Two points determine exactly one line.”

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Unique Plane PostulateThrough any 3 noncollinear points

there is a unique plane.

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Flat Plane PostulateIf two points are in a plane, then the

line containing them is in the plane.

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Dimension PostulateGiven a line in a plane, there is at least

one point in the plane that is not on the line.

Given a plane in space, there is at least one point in space not on the plane.

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Assignment:

pages 14 – 15, # 9 – 48