point point: described as the basic unit of geometry; it is infinitely small, it has only location...
TRANSCRIPT
POINTPOINT: described as the basic unit of geometry; it is infinitely small, it has only location and no size; grain of sand or ballpen tip illustrates a point.
Examples:
Point A or Point B.
undefineundefined termd term
.A.B
LINELINE: described as a straight continuous arrangement of an infinite number of points; has infinite length but no thickness; extends in two opposite directions;
Name a line by determining 2 points on the line:
undefineundefined termd term
A
BAB or BA%&%&&%&&%&&%&&%&&%&&%&&%&&%&&%&&%&&%&&%& &%&
PLANEPLANE: described as having length and width but no thickness; like a flat surface that extends forever along its length and width; represented by a four-sided figure.
undefineundefined termd term
A
B.X.Y
Plane ABX
or Plane P
COLLINEARCOLLINEAR: Being on the same line / Collinear points are points that lie on the same line.
COPLANARCOPLANAR: Being on the same plane / Coplanar points/lines are points/lines that lie on the same plane.
Is it necessary to say “two collinear points”?
No. Two points already determine a line. A line exists connecting any two distinct points.Can a point and a line be coplanar?
Yes.
SPACESPACE: Defined as the set of all points.
A
B.X.Y
Two distinct points determine a line.Two distinct points determine a line. Three distinct collinear points determine Three distinct collinear points determine
at least 1 plane.at least 1 plane.
Three distinct non-collinear points Three distinct non-collinear points determine a unique plane.determine a unique plane.
How many planes are determined by 4 How many planes are determined by 4 non-collinear points?non-collinear points?
How many planes are determined by 5 How many planes are determined by 5 points, three of which are collinear?points, three of which are collinear?
A line intersecting a pointA line intersecting a point
Two intersecting linesTwo intersecting lines
A line contained in a planeA line contained in a plane
A plane intersecting a line at exactly A plane intersecting a line at exactly one pointone point
Two distinct planes that do not Two distinct planes that do not intersectintersect
Two intersecting (but not Two intersecting (but not overlapping) planesoverlapping) planes
How do we define How do we define ““BETWEENBETWEEN””??
A B C D EG
F
H
B is between A and C.C is between A and D.
“between-ness” assumes that the points are collinear.
F is NOT between B and E.H is NOT between D and E.
LINE SEGMENTLINE SEGMENT: Defined as part of a line; consists of two points (endpoints) and all points between them
Segment AB (point A and point B as endpoints)
A
B
Segment AB
AB or BA
How do we measure segments?How do we measure segments?
mAB 3
the measure of a segment is usually written on the middle portion of the segment.
A B C D E
3 2312
AB 3
mCD 2
CD 2mDE 12
DE 12
How do we measure segments?How do we measure segments?
mAC 6
What is AC? BD? BE? AE?
A B C D E
3 2312
AC 6
mBD 5
BD 5mBE 17
BE 17
mAE 20
AE 20
If A, B, and C are collinear such that B
is between A and C, then AB + BC =
AC.
SEGMENT ADDITION POSTULATESEGMENT ADDITION POSTULATE
A B C
CONGRUENT SEGMENTSCONGRUENT SEGMENTS: Two segments are congruent segments if and only if they have the same length.
AB CDIf segment AB is CONGRUENT with segment CD,
then the measure of length of segment AB is EQUAL to the measure of length segment CD.
mAB mCD AB CD
Congruent figures!
Equal measures!
MIDPOINT OF A SEGMENTMIDPOINT OF A SEGMENT: If X is the midpoint of , then X is a point on such that AX=XB.
ABABAB
AB AB
The midpoint of a segment divides the segment into 2 congruent parts. It becomes a segment bisector.
A X B
ABABAB
A B
X
Sometimes. Point X is a midpoint if it lies on segment AB.
Given:
Segment A, where AX is equal to XB.
Therefore, AX is congruent to XB.
Is Point X a midpoint of Segment AB?
Always, Sometimes, Never?