POINTS, LINES AND PLANES
OBJECTIVES SWBAT: To understand basic terms of geometry. To understand and apply basic postulates of geometry.
What is Geometry? Geometry is the visual study of shapes, sizes, patterns, and positions. It occurred in all cultures, through at least one of these five strands of human activities: 1. building/structures 2. motion 3. navigating 4. art/patterns 5. measurement
A POINT is an exact location on a graph, shape or in space.
LINE A LINE is a series of points that extends in 2 opposite directions without end. Take a pearl necklace and stretch it out. The pearls are like points on a line.
PLANE A PLANE is a flat surface that has no thickness and goes on forever in all directions. Imagine sitting on an island in the middle of the ocean. No matter which way you look…all you see is water…forever.
TO NAME A POINT- WE USE A CAPTIAL LETTER .X
TO NAME A LINE- USE ANY 2 POINTS ON THE LINE LINE RT or LINE ST or LINE RS R T S RT RS
POINTS ON THE SAME LINE ARE CALLED COLLINEAR POINTS A, B, AND Y ARE COLLINEAR . . Y . B A
TO NAME A PLANE WE USE 3 OR 4 NONCOLLINEAR POINTS PLANE WAG or XAG or WXA . .A X Q .W .G PLANES CAN BE NAMED USING 1 LETTER …. PLANE Q
THE INTERSECTION OF 2 LINES IS A POINT S IS THE INTERSECTION OF THE 2 LINES
LINE AB IS CONTAINED IN PLANE Q
LINE XY INTERSECTS PLANE Q AT POINT X . X
THE ARROW INTERSECTS THE TARGET AT 1 POINT
Lines YB and XZ do not intersect . Y . B X
THE INTERSECTION OF 2 PLANES IS A LINE D G B C E E G H C F
POINTS AND LINES CONTAINED IN THE SAME PLANE ARE CALLED COPLANAR Y W. S. P X G.
A postulate or axiom is an accepted statement of fact.
Through any two points there is exactly one line. Postulate 1-1 Through any two points there is exactly one line. Postulate 1-2 If two lines intersect, then they intersect in exactly one point. B A X
If two planes intersect, then they intersect in exactly one point. Postulate 1-3 If two planes intersect, then they intersect in exactly one point. Postulate 1-4 Through any three noncollinear points there is exactly one plane.