1/18/ : 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.

1/18/ : The Building Blocks of Geometry Undefined Terms

1/18/ : The Building Blocks of Geometry Points Models of points 0 dimensional (have no size) -Dots -Stars in the sky -Cities on a map

1/18/ : The Building Blocks of Geometry Points Naming points - Use capital letters A

1/18/ : The Building Blocks of Geometry Lines Perfectly straight extending infinitely without thickness. Models of Lines - roads - hallway - edge of a box 1 dimensional

1/18/ : The Building Blocks of Geometry Naming Lines l Line l

1/18/ : The Building Blocks of Geometry Naming Lines A B Line AB or BA

1/18/ : The Building Blocks of Geometry Planes Infinite, flat surface without thickness. 2 dimensional Models of Planes -desktop -wall -rooftop

1/18/ : The Building Blocks of Geometry Drawing Planes

1/18/ : The Building Blocks of Geometry Naming Planes Plane R R

1/18/ : The Building Blocks of Geometry Naming Planes Plane PQR, PRQ, RPQ, RQP, QRP or QPR P R Q

1/18/ : The Building Blocks of Geometry Collinear Points Defn:Three or more points are collinear iff they are on the same line. ABC A, B and C are collinear.

1/18/ : The Building Blocks of Geometry Coplanar Points Defn: Four or more points are coplanar iff they are on the same plane.

1/18/ : The Building Blocks of Geometry Coplanar Points P, Q, R and S are coplanar points. P R Q S

1/18/ : The Building Blocks of Geometry Segments Defn: 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.

1/18/ : The Building Blocks of Geometry Segments AB AB This is not a segment!!!

1/18/ : The Building Blocks of Geometry Segments AB The segment with endpoints A and B: denoted AB or BA

1/18/ : The Building Blocks of Geometry Rays Defn: 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.

1/18/ : The Building Blocks of Geometry Rays Y Z The ray with endpoint Y containing Z: denoted YZ (may not be denoted ZY or ZY).

1/18/ : The Building Blocks of Geometry Angles Defn: 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.

1/18/ : The Building Blocks of Geometry Angles

1/18/ : The Building Blocks of Geometry Angles vertex of the angle sides of the angle

1/18/ : The Building Blocks of Geometry Naming an Angle There 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.

1/18/ : The Building Blocks of Geometry Naming Angles A B C 1

1/18/ : The Building Blocks of Geometry Naming Angles A B C BB 1

1/18/ : The Building Blocks of Geometry Naming Angles A B C   ABC or  CBA 1

1/18/ : The Building Blocks of Geometry Naming Angles A B C  11 1

1/18/ : The Building Blocks of Geometry 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.

1/18/ : The Building Blocks of Geometry Postulates A postulate is a statement that is accepted as being true without proof.

1/18/ : The Building Blocks of Geometry Complete Activity 1.1 on page 12. You may work in pairs.

1/18/ : The Building Blocks of Geometry Intersecting Lines Postulate If two lines intersect, then their intersection is a point.

1/18/ : The Building Blocks of Geometry Intersecting Planes Postulate If two planes intersect, then their intersection is a line.

1/18/ : The Building Blocks of Geometry Unique Line Postulate Through 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.”

1/18/ : The Building Blocks of Geometry Unique Plane Postulate Through any 3 noncollinear points there is a unique plane.

1/18/ : The Building Blocks of Geometry Flat Plane Postulate If two points are in a plane, then the line containing them is in the plane.

1/18/ : The Building Blocks of Geometry Dimension Postulate Given 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.

1/18/ : The Building Blocks of Geometry Assignment: pages 14 – 15, # 9 – 48