Point
Undefined, labeled with a capital letter in vicinity
Line
Undefined, arrows to represent infinite lengthName: any letter two points on the line, draw a line over Ex. <---> <---> TK is the same as KT
Plane
Undefined, extends forever, made up of more than 2 points (non collinear)Name: with capital letter(s)
Collinear
Points on the same line (even if you can't see line)
Coplanar
Points on the same plane
Line Segment
Part of a line with two endpointsName: letter endpoints, draw segment over(add 'm' for measure)Ex.---- ---- AB is the same as BA
Ray
A part of a line, with one endpoint, that continues without end in one directionName: Endpoint and any other point on ray, draw right facing arrow (ex. --->)A ray always starts at an endpointEx.<---m---n---p Possible names= ray PM or ray PNCannot be ray NM because P is the endpoint
Equal
same value
Congruent
same size and shape (shown using marks)
Bisect
to divide into two equal parts(a line cannot be bisected)
Midpoint
The point that bisects a segmentMust be two congruent segments (marked with lines)Ex.----II----T----II-----. T is the midpoint if there are the same number of marks
Midpoint formula
(x₁+x₂), (y₁+y₂)------- ------- 2 2Solves for the the coordinates for the midpoint of a segment
Midpoint formula: if given midpoint and one endpoint
Ex. (-9,4)= endpoint and (2,-5)= midpoint(-9 + x)/2 , (4+y)/2 = (2,5)split up into 2 equations using the midpoint coordinates1) (-9 + x)/2 = 2 x=13 Missing endpoint= (13,-14)2) (4 + y)/2 = -5 y=-14
How to divide a segment into 4
1) Find the midpoint of the segment2) Find the midpoints of the two new segments
How to divide a segment into 3
To find the 1/3 point= x2-x1 y2-y1( ------ ------ ) 3 , 3To find the 2/3 point=(2/3 (x2-x1) , 2/3 (y2-y1)
segment bisector
a segment, ray, line, or plane that intersects a segment at its midpoint
Undefined terms of Geometry
point, line, plane