TEKS Focus: (4)(A) Distinguish between undefined terms, definitions, postulates, conjectures, and theorems. (1)(D) Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate. (1)(F) Analyze mathematical relationships to connect and communicate mathematical ideas.
What is a point? What is a point? What is a plane? What is a plane?
The most basic figures in geometry are undefined terms, which cannot be defined by using other figures. The undefined terms point, line, and plane are the building blocks of geometry. Building blocks refers to the basic foundation of geometry.
Vocabulary Term DiagramNameDefinition A point names a location and has no size. It is represented by a dot. A line is a straight path that has no thickness and extends forever. A plane is a flat surface that has no thickness and extends forever. P XY l A B C R Point Line Plane P (use capital letters to name points) Line l or Plane R or Plane ABC
Vocabulary Term DiagramNameDefinition A segment or line segment is the part of a line consisting of two points and all the points between. An endpoint is a point at the one end of a segment or starting point of a ray. A ray is a part of a line that starts at an endpoint and extends forever in one direction. Opposite rays are two rays that have a common endpoint and form a line. AB CD RSSREFG Segment Endpoint Ray Opposite Rays or C and D (use capital letters to name points)
Points that lie on the same line are collinear. The opposite of collinear is noncollinear. K, L, and M are collinear. K, L, and N are noncollinear. M K L N
Coplanar points and lines lie in the same plane. The opposite of coplanar is noncoplanar. This point is noncoplanar to the plane containing the other 4 points.
A postulate, or axiom, is an accepted statement of fact without proof. Postulates about points, lines, and planes help describe geometric properties.
The intersection of two or more geometric figures is the set of points the figures have in common. Space is the set of all points in three dimensions.
Discuss the following questions with your partners and answer always, sometimes, or never: 1. Two points are ___________________ collinear. 2. Two lines are __________________ coplanar. Answers: 1 is always; 2 is sometimes.
Draw and label a ray with endpoint F that passes through G. F G F G FG
A. Name four coplanar points. B. Name three lines. A, B, C, D Possible answer: AE, BE, CE
Refer to the architectural design of the Central Library building. 1.Name four coplanar points. 2. Name three lines. K, L, M, and N all lie in plane R.
A. Sketch two lines intersecting in exactly one point. B. Sketch a figure that shows a line that lies in a plane.
Sketch a figure that shows two lines intersect in one point in a plane, but only one of the lines lies in the plane. Note: Use a dashed line to show the hidden parts of any figure that you are drawing. A dashed line will indicate the part of the figure that is not seen.
Sketch a figure that shows a line that intersects two parallel planes.
Sketch a figure that shows three coplanar lines that intersect in three different points.
FOR EXTRA EXAMPLES NOT USED IN COMPOSITION BOOK FOLLOW, LOG-ON TO YOUR PEARSON ACCOUNT AND GO THROUGH UNIT 1 LESSON 1-1BEFORE YOU DO THE ON-LINE HW AND THE WRITTEN HW.