Bellringer
– Solve each system of equations (Use either elimination or
substitution)
1. y = x + 5
y = -x + 7
2. y = 2x – 4
y = 4x - 10
1-2 Points,
Lines, and
Planes
Definitions
– Space – the set of all points
– Line – a series of points that extends in two opposite directions
without end.
– 𝐴𝐵 read “line AB”
– Collinear - Points that lie on the same line.
– Plane – a flat surface that has no thickness.
– A plane contains many lines and extends without end in the directions of all its lines
– Coplanar – Points and lines in the same plane
Naming Lines
– Name line m in three other ways
– Name line n in three other ways
Collinear?
– Name 3 collinear points
– Name 3 noncollinear points
Naming a plane
– Must be named by at least 3
noncollinear points in the plane
1. List 3 different names for the plane
represented by the front of the cube.
Postulates
- an accepted statement of fact
– Postulate 1-1 : Through any two points there is exactly one line
A
B
t
– Line t is the only line that passes through points A and B
– Postulate 1-2 : If two lines
intersect, then they intersect in exactly one point
B
A
𝐴𝐸 𝑎𝑛𝑑 𝐵𝐷 intersects at C
C
D
E
– Postulate 1-3 : If two planes intersect, then they intersect in exactly one
line.
– Plane RST and plane STW intersect in 𝑆𝑇
Finding the Intersection of Two
Planes
– What is the intersection of plane SWVR and
plane RVUQ?
– 𝑹𝑽
– What it the intersection of plane PTUQ and
plane PSWT?
– 𝑷𝑻
– What is the intersection of plane TWVU and
plane PSRQ?
– NONE
Postulate 1-4
Through any three noncollinear points there
is exactly one plane
– Shade the plane that contains P, Q,
and U.
– Name another point that is coplanar
with points P, Q, and U.
– T
Homework
– Pg. 13 - 14
– #’s 2 - 36 even