Download Unit 1 : Point, Line and Plane Geometry Definitions (1.21.6) p.1050

geo_definitions.notebook
August 10, 2015
Unit 1 : Point, Line and Plane Geometry Definitions (1.2­1.6) p.10­50
Euclid: The father of Geometry
Undefined Terms: point, line, and plane are not defined because no known words can be used to describe them.
Point: no dimensions, usually represented by a dot (points are usually labeled with capital letters)
A
Point A
Line: extends in 2 dimensions, usually represented by a straight line with arrows on each end to indicate it goes on forever in both directions
B
C
l
BC
line BC
line l
CB
Plane: extends in 2 dimensions, usually represented by a shape that looks like a slanted rectangle (it continues in all directions forever)
Collinear points: points on the same line
D
E
F
G
Coplanar points: points on the same plane
Intersect: 2 figures intersect if they have one or more points in common
Intersection: the set of all points the figures have in common
Parallel Lines (//): 2 lines in the same plane that never intersect (Use arrows on the picture to label parallel lines)
Perpendicular Lines ( ): 2 lines that intersect and form 4 right angles
(Put a box between the two lines to label right angles)
Skew Lines: 2 lines not in the same plane that never intersect
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Segment (or line segment): a line with two endpoints
F
D
segment DF
DF
FD
The length of DF is shown by DF
(no bar above the letters)
Ray: a line with only one endpoint
G
ray GH
GH
H
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Postulate (axiom): accepted rules or facts
Theorem: Conjectures (rules) that are proven Congruent segments(≅): segments that have the same length
(put tic marks on congruent segments)
Q
S
R
QR ≅ RS
Midpoint: a point that divides (bisects) a segment into 2 congruent segments
J is the midpoint of IK
J
I
K
therefore IJ ≅ JK
Segment Bisector: a segment, line, or ray that intersects a segment at its midpoint
M
L
p
N
line p bisects LN at point M
therefore M is the midpoint of LN
and LM ≅ MN
Parallel line Postulate: Given a point and a line there is only one line passing through the given point parallel to the given line. .
Explain how there could be controversy with this postulate. 3
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Angle: consists of 2 different rays that have the same endpoint.
Sides: are the rays that form the angle
Vertex: the endpoint where the angle is formed
<ABC
A
<CBA
<1
1
B
and since there is only 1 angle at point B then you can say <B
C
Congruent Angles(≅): angles that have the same measure
put arcs in the angles that are congruent
3
< 2 ≅ < 3
2
Protractor Postulate: used to measure the degree of an angle from 0­1800
Measure of angle ABC: written as m<ABC
Angle Bisector: a ray that divides and angle into 2 congruent angles
B
BC Bisects < ABD
therefore <ABC ≅ <CBD
D
A
C
Perpendicular Bisector:
a line, segment, or ray that intersects a segment at its midpoint and forms right angles (90 0)
l
Line l is a perpendicular bisector of AB because M is the midpoint of AB and right angles are formed
A
M
B
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Classifying Angles
Acute Angle: measures between 0 and 90 0
Right Angle: measures exactly 90 0
Obtuse Angle: measures between 90 and 180 0
Straight Angle: measures exactly 180 0 Adjacent Angles: angles that share a common vertex and a side, but no common interior points
T
Y
X
L
M
N
P
<LMN is adjacent to <NMP
they are not and do not have to be congruent
W
Z
<XTW is adjacent to <WTZ
and <WTY
<YTZ is adjacent to <ZTW
and <
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Vertical angles: opposite angles formed when 2 lines, rays, or segments intersect 2
1
3
Vertical angles are congruent (≅)
Ex: <1≅<3 and <2≅<4
4
Linear Pair: 2 adjacent angles whose noncommon sides are opposite rays
Linear pairs add to 180 0
<5 and <6 are a linear pair, so m<5 + m<6 = 180
5
6
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Complementary angles:
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2 angles whose sum is 900
1
2
4
3
<1 and <2 are complementary adjacent angles therefore m<1 + m<2 = 90
Supplementary angles:
<3 and <4 are complementary nonadjacent angles therefore m<3 + m<4 = 90
2 angles whose sum is 1800
8
5
6
<5 and <6 are supplementary adjacent angles therefore they are a linear pair and m<5 + m<6 = 180
7
<7 and <8 are supplementary
nonadjacent angles therefore
m<7 + m<8 = 180
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