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U SING U NDEFINED T ERMS AND D EFINITIONS. Point. A. A. A point has no dimension. It is usually represented by a small dot. •. U SING U NDEFINED T ERMS AND D EFINITIONS. Line or AB. A line extends in one dimension. It is usually represented
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USING UNDEFINED TERMS AND DEFINITIONS Point A A A point has no dimension. It is usually represented by a small dot. •
USING UNDEFINED TERMS AND DEFINITIONS Line or AB 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.
USING UNDEFINED TERMS AND DEFINITIONS 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.
USING UNDEFINED TERMS AND DEFINITIONS A C B M Coplanar points are points that lie on the same plane. Plane M or plane ABC
Naming Collinear and Coplanar Points H G F E D • Name three points that are collinear. • Name four points that are coplanar. • Name three points that are not collinear. SOLUTION • Points D, E, F lie on the same line, so they are collinear. • Points D, E, F, and G lie on the same plane, so they are coplanar. Also, D, E, F, and H are coplanar. • There are many correct answers. For instance, points H, E, and G do not lie on the same line.
USING UNDEFINED TERMS AND DEFINITIONS Another undefined concept in geometry is the idea thata point on a line is between two other points on the line. You can use this idea to define other important termsin geometry.
USING UNDEFINED TERMS AND DEFINITIONS Consider the lineAB (symbolized by AB). The line segment or segmentAB (symbolized by AB) consists of the endpointsA and B, and all points on AB that are between A and B.
USING UNDEFINED TERMS AND DEFINITIONS Note that AB is the same as BA, and ABis the same as BA. However, AB and BA are not the same. They have different initial points and extend in different directions. The rayAB (symbolized by AB) consists of the initial pointA and all points on AB that lie on the same side of A as point B.
USING UNDEFINED TERMS AND DEFINITIONS If C is between A and B, then CA and CB 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.
Drawing Lines, Segments, and Rays 1 2 3 4 K Draw JK. J Draw KL. L Draw LJ. Draw three noncollinear points J, K, L. Then draw JK, KL and LJ. SOLUTION Draw J, K, and L
Drawing Opposite Rays So, XM and XN are opposite rays. So, XP and XQ are opposite rays. Draw two lines. Label points on the lines and name two pairs of opposite rays. SOLUTION 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.
SKETCHING INTERSECTIONS OF LINES AND PLANES 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.
Sketching Intersections Sketch a line that intersects a plane at one point. SOLUTION Draw a plane and a line. Emphasize the point where they meet. Dashes indicate where the line is hidden by the plane.
Sketching Intersections Sketch two planes that intersect in a line. SOLUTION Draw two planes. Emphasize the line where they meet. Dashes indicate where one plane is hidden by the other plane
