Beginning terms

1. A point has no dimension. It is usually represented by a small dot. • A Point A U SING U NDEFINED T ERMS AND D EFINITIONS

2. A line extends in one dimension. It is usually represented by a straight line with two arrowheads to indicate that the line extends without end in two directions. Collinear points are points that lie on the same line. Line or AB U SING U NDEFINED T ERMS AND D EFINITIONS

3. A plane extends in two dimensions. It is usually represented by a shape that looks like a table or a wall, however you must imagine that the plane extends without end. U SING U NDEFINED T ERMS AND D EFINITIONS

4. Coplanar points are points that lie on the same plane. Plane M or plane ABC A C M B U SING U NDEFINED T ERMS AND D EFINITIONS

5. S OLUTION • Points D , E , F lie on the same line, so they are collinear. • There are many correct answers. For instance, points H , E , and G do not lie on the same line. • Points D , E , F , and G lie on the same plane, so they are coplanar. Also, D , E , F , and H are coplanar. • Name three points that are collinear. • Name four points that are coplanar. • Name three points that are not collinear. Naming Collinear and Coplanar Points G H F E D

6. Another undefined concept in geometry is the idea that a point on a line is between two other points on the line. You can use this idea to define other important terms in geometry. U SING U NDEFINED TERMS AND DEFINITIONS

7. The line segment or segment AB (symbolized by AB ) consists of the endpoints A and B , and all points on AB that are between A and B . U SING U NDEFINED T ERMS AND D EFINITIONS Consider the line AB (symbolized by AB ).

8. The ray AB (symbolized by A B ) consists of the initial point A and all points on AB that lie on the same side of A as point B . Note that AB is the same as BA , and AB is the same as BA . However, A B and B A are not the same. They have different initial points and extend in different directions. U SING U NDEFINED T ERMS AND D EFINITIONS

9. If C is between A and B , then C A and C B are opposite rays . Like points, segments and rays are collinear if they lie on the same plane. So, any two opposite rays are collinear. Segments, rays, and lines are coplanar if they lie on the same plane. U SING U NDEFINED T ERMS AND D EFINITIONS

10. Draw three noncollinear points J , K , L . Then draw JK, KL and L J . S OLUTION Draw J , K , and L Drawing Lines, Segments, and Rays 1 2 3 4 Draw JK . Draw LJ . K L J Draw KL .

11. Draw two lines. Label points on the lines and name two pairs of opposite rays. S OLUTION Points M , N , and X are collinear and X is between M and N . Points P , Q , and X are collinear and X is between P and Q . Drawing Opposite Rays So, XM and XN are opposite rays. So, XP and XQ are opposite rays.

12. S KETCHING I NTERSECTIONS OF L INES AND P LANES Two or more geometric figures intersect if they have one or more points in common. The intersection of the figures is the set of points the figures have in common.

13. Sketch a line that intersects a plane at one point. S OLUTION Draw a plane and a line. Emphasize the point where they meet. Dashes indicate where the line is hidden by the plane. Sketching Intersections

14. Sketch two planes that intersect in a line. S OLUTION Draw two planes. Emphasize the line where they meet. Dashes indicate where one plane is hidden by the other plane Sketching Intersections