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Math Definitions Chapter 1 Pearson Geometry


undefined, object
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deductive reasoning
takes known info to get to next step, each fact leads to next conclusion
inductive reasoning
base hypothesis on what is seen so far
collinear points
points that are on the same line
coplanar points
points that are on the same plane
set of all points
postulates (axioms)
accepted idea om geometry
idea that has to be proven or justified
Postulate (a)
through any 2 points there is exactly one line (2 points determine a line)
Postulate (b)
If 2 lines intersect, they intersect at exactly one point
Postulate (c)
If 2 planes intersect, they intersect at exacly one line
Postulate (d)
Through any 3 noncollinear points there is exactly 1 plane
(three noncollinear points determine a plane)
a part of a line consisting of 2 endpoints and all the points in between them
a part of a line consisting of 1 endpoint and all the points of the line on 1 side of the endpoint
opposite rays
2 collionear rays with the same endpoint
opposite rays always form a line
parallel lines
coplanar lines that do not intersect
skew lines
noncoplanar lines
parallel planes
planes that never meet
Ruler Postulate:
If you have a number line, all the points on that line have a 1 to 1 correspondence to the numbers on the line
2 segments of the same length
If _AB is congruent to _CD then AB=CD and if AB=CD then _AB=_CD
a midpt. of a segment is a point that divides a segment into 2 congruent segments (or two segments of equal length)
B is the midpt. of _AC if _AB=_BC and B is in between A and C (and visa versa)
Segment Addition Postulate
If A,B,C are collinear and B is between A and C then AB+BC=AC
union of 2 rays w/ a common endpt.
the rays are the sides of the angle. The endpt. is the vertex of the angle
Protractor Postulate
If you look at all the possible angle measures between 0 and 180 and all the possible sized angles between a ray folded onto itself and a pair of opposite rays, there will be a 1 to 1 correspondence between the angle measures and the angles themselves
Angle Addition Postulate
If a point B is in the interior of <AOC then m<AOB + m<BOC = m<AOC
If <AOC is a straight angle then m<AOB+m<BOC =180
Congruent Angles
angles with the same measure
a way to create geometric objects using a straightedge and a compass
perpendicular lines
lines that intersect to form right angles
perpendicular bisector of a segment
a line, segment or ray that is perpendicular to a segment at its midpoint

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