Warm Up Name all points on the Coordinate Plane and Note their Corresponding Quadrant or Axis..

Euclidean and Non Euclidean Geometry! So what’s the difference?

What do we know about it?

What do we know about it?

And..

Undefined Terms Words that do not have formal definitions but there is an agreement about what they mean.

Point

Line

Plane

Think, Pair, Share Discuss what Points, Lines, and Planes are and explain what an undefined term is.

Collinear Points

Coplanar Points

Think, Pair, Share What does it mean to be Collinear or Coplanar?

EXAMPLE 1 Name points, lines, and planes a. Give two other names for PQ and for plane R. b. Name three points that are collinear. Name four points that are coplanar. SOLUTION Other names for PQ are QP and line n. Other names for plane R are plane SVT and plane PTV.

EXAMPLE 1 Name points, lines, and planes b. Points S, P, and T lie on the same line, so they are collinear. Points S, P, T,and V lie in the same plane, so they are coplanar.

GUIDED PRACTICE Think, Write, Pair, Share 1. Use the diagram in Example 1. Give two other names for ST . Name a point that is not coplanar with points Q, S, and T. ANSWER TS, PT; point V

Terms that can be described using known terms like Point or Line Defined Terms Terms that can be described using known terms like Point or Line

Segment

Ray

Opposite Ray

EXAMPLE 2 Name segments, rays, and opposite rays a. Give another name for GH . b. Name all rays with endpoint J . Which of these rays are opposite rays? SOLUTION a. Another name for GH is HG . b. The rays with endpoint J are JE , JG , JF , and JH . The pairs of opposite rays with endpoint J are JE and JF , and JG and JH .

GUIDED PRACTICE Think, Write, Pair, Share 2. Give another name for EF ANSWER FE 3. Are HJ and JH the same ray ? Are HJ and HG the same ray? Explain. ANSWER No; the rays have different endpoints. Yes; points J and G lie on the same side of H.

Intersection

EXAMPLE 3 Sketch intersections of lines and planes a. Sketch a plane and a line that is in the plane. b. Sketch a plane and a line that does not intersect the plane. c. Sketch a plane and a line that intersects the plane at a point. SOLUTION a. b. c.

EXAMPLE 4 Sketch intersections of planes Sketch two planes that intersect in a line. Draw: a vertical plane. Shade the plane. STEP 1 SOLUTION Draw: a second plane that is horizontal. Shade this plane a different color. Use dashed lines to show where one plane is hidden. STEP 2 Draw: the line of intersection. STEP 3

Think, Pair, Share What does ‘defined’ mean? Discuss the differences between Rays, Opposite Rays, and Intersections.

Quick Write In at least three sentences, compare and contrast points, lines, and planes.

Postulate- a statement that is accepted as true without proof. Through any two points there is exactly one line. Through any three non-collinear points there is exactly one plane containing them If two points lie in a plane, then the line containing those points is on the plane If two lines intersect, then they intersect in exactly one point If two planes intersect, then they intersect in exactly one line. Conjecture- A statement you believe to be true based on inductive reasoning. Theorem- a statement that can be proven true.