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1.1 Points, Lines, Planes, and Angles
Citation preview
Solve each equation.
1. 5(x – 6) = 40 2. 5b = 2(3b – 8) 3. 2y + 6y = 15 – 2y + 8
4. 4x + 8 > 20
Absolute Value Equations and Inequalities
Solve each inequality.
6. 4(t – 1) < 3t + 55. 3a – 2 a + 6>–
1. 5(x – 6) = 40 2. 5b = 2(3b – 8)
= 5b = 6b – 16
x – 6 = 8 –b = –16x = 14 b = 16
Solutions
Absolute Value Equations and Inequalities
5(x – 6)5
405
5. 3a – 2 a + 6 6. 4(t – 1) < 3t + 53a – a 6 + 2 4t – 4 < 3t + 5
2a 8 4t – 3t < 5 + 4a 4 t < 9
3. 2y + 6y = 15 – 2y + 8 4. 4x + 8 > 202y + 6y + 2y = 15 + 8 4x > 12
10y = 23 x > 3y = 2.3
>–>–>–>–
1.1 Points, Lines, Planes, and Angles
Vocabulary…• Point – A location in space• Line – A geometric shape made up of at least two points
and had no width or thickness• Collinear – Points on the same line.• Plane – A flat surface made up of at least three non-
collinear points, or a line and one non-collinear point. It has an infinite length and width but no depth.
• Undefined Term – Any term that has been defined using examples and descriptions instead of a mathematical proof.
• Space – A boundless three dimensional set of all points. It can contain lines and planes.
POINT
• PDrawn: as a dotNamed by: a capital letterFacts: has neither shape nor size
LINE
Drawn: with an arrowhead at each endNamed by: the letters representing two
points on the line OR a lowercase script letter
Fact: there is exactly one line through any two points
Words/Symbols: line n, line AB, or AB, line BA or BA
PLANE
Drawn: as a shaded, slanted, 4-sided figureNamed by: a capital script letter OR by
names three noncollinear pointsFact: There is exactly one plane through any
three noncollinear points. Words/Symbols: plane T, plane XYZ, plane
XZY, plane YXZ, plane YZX, plane ZXY, plane ZYX
X Y
Z
Example 1
• Use the figure to name each of the following.
a. A line containing point K
b. A plane containing point L.
JK
L
M
B
a
EX 2. Visualization…
• Name the geometric shape modeled by each object.
a. The long hand on a clockb. A 10 x 12 patioc. The location where the corner of the
driveway meets the road
Example 3
• Draw and label a figure for each relationship.
• Plane R containing lines AB and DE intersect at point P. Add point C on plane R so that it is not collinear with AB or DE.
Example 4a
S
B
C
D
E
A
How many planes appear in this figure?
Example 4b
S
B
C
D
E
A
Name three points that ARE collinear.
Example 4c
S
B
C
D
E
A
Are points A, B, C and D coplanar?
Example 4d
S
B
C
D
E
A
At what point do DB and CA intersect?
You try…
• Page 9 #’s 1-12
Homework…
• Page 9 #’s 13 – 20