Math Definitions Chapter 1 Pearson Geometry
Terms
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
- space
- set of all points
- postulates (axioms)
- accepted idea om geometry
- theory
- 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) - segment
- a part of a line consisting of 2 endpoints and all the points in between them
- ray
- 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
- congruent
-
2 segments of the same length
If _AB is congruent to _CD then AB=CD and if AB=CD then _AB=_CD - midpoint
-
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
- angle
-
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
- constructions
- 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