some basic figures
DESCRIPTION
Some Basic Figures. Points, Lines, Planes, and Angles. Objectives. Definitions and Postulates. Geometry. Segments, Rays, and Distance. Segment- Ray - Opposite Rays- Length of a segment- distance between the two endpoints. Vocabulary. - PowerPoint PPT PresentationTRANSCRIPT
Some Basic Figures
Points, Lines, Planes, and Angles
Objectives
Definitions and
PostulatesGeometry
Segments, Rays, and Distance
1.Segment-
2.Ray -
3.Opposite Rays-
4.Length of a segment- distance between the two endpoints
Vocabulary1.Congruent- two shapes that have the same
size and shape.
2.Congruent Segments-segments that have equal lengths
3.Midpoint of a segment-the point that divides the segment into two congruent segments.
4.Bisector of a segment- a line, segment, ray, or plane that intersects the segment at its midpoint.
Postulate 1 (Ruler Postulate)
1.Once a coordinate system has been chosen in this way, the distance between any two points equals the absolute value of the difference of their coordinates.
Postulate 2 (Segment Addition
Postulate)If B is between A and C, then AB + BC = AC
AB
C
AnglesGeometry
Postulates and
Theorems Relating
Points, Lines and Planes
Vocabulary • Congruent Angles-angles that have
equal measures
• Adjacent Angles-two angles in a plane that have common vertex and a common side but no common interior points.
Vocabulary• Bisector of an angle- the ray that
divides that angle into two congruent adjacent angle.
Postulate 3 (Protractor Postulate)
Postulate 4 (Angle Addition Postulate)
Postulate 5A line contains at least two points; a plane contains at least three points not all in one line; space contains at least four points not all in one plane.
Postulate 6• Through any two points there is
exactly one line.
Postulate 7• Through any three points there is at
least one plane, and through any three noncollinear points there is exactly one plane.
Postulate 8• If two points are in a plane, then the
line that contains the points is in that plane.
Postulate 9• If two planes intersect, then their
intersection is a line.
TheoremsTheorem 1
If two lines intersect, then they intersect in exactly one point.Theorem 2
Through a line and a point not in the line there is exactly one planeTheorem 3
If two lines intersect, then exactly one plane contains the lines