Give an example of a point, line and plane that can be found in the classroom.
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Transcript of Give an example of a point, line and plane that can be found in the classroom.
Opening Activity
Give an example of a point, line and plane that can be found in the classroom.
1.1 POINTS, LINES, & PLANES
Geometry Online Textbook
Foldable Activity
What is a definition?
Known words used to describe a new word
Undefined terms – not formally defined
There are 3 in geometry.
Point Line Plane
Point
1. Has no dimension (no length, width,
thickness)
2. Usually represented by a
dot
3. Named using one capital letter, B
LineExtends forever in one dimension (length)Has an arrowhead on each end representing the fact that it goes on foreverConsists of an infinite amount of points
Always straight
Named with a lowercase script letter or by 2 points on the line
A B
l
Can be called:
Line l
Line AB or AB
Line BA or BA
PlaneExtends forever in 2 dimensions (length &
width)
A flat surface consisting of
infinitely many points
Usually represented by a 4-sided figure
Named with a capital script letter or 3 points on the
surface of the plane
A
BC
W Can be named:
Plane W
Plane ABC, plane BCA, plane CBA, etc.
More Definitions
Collinear points – points that lie on the same line
Coplanar points – points that lie on the same plane
Space – a boundless, three-dimensional set of all points. Space can contain lines and planes.
IDENTIFY AND NAME THE FOLLOWING:
POINT LINE PLANE COLLINEAR POINTS NONCOLLINEAR POINTS COPLANAR POINTS NONCOPLANAR POINTS
Practice
Assignment
Handout
Warm up
Practice
1.2 LINEAR MEASURES
Geometry Online Textbook
User Name:GEOVA05
Password: crAju4re
Line Segment (or segment)
A section of a line that has 2 endpoints
Named by its endpoints. AB or BA
The length or measure of AB is written as AB.
A B
Example:
Find the length of AB using the ruler.
A B
BETWEENNESS OF POINTS
AB + BC = AC.
If AB + BC = AC, then B is between A & C.
PRACTICE
Find the value of the variable and LM if L is between N and M.
1. NL = 5x, LM = 3x, and NL = 15
2. NL = 6x – 5, LM = 2x + 3, and NM = 30
CONGRUENT SEGMENTS
Two segments having the same measure are congruent.
is read is congruent to. (Red slashes indicate t he segments are congruent.)
2 cm 2 cm
Independent Practice
Handout Homework Page 17 22 – 39 all
1.3 DISTANCE AND
MIDPOINTS
Geometry Online Textbook
User Name:GEOVA05
Password: crAju4re
Warm up
Practice
DISTANCE BETWEEN TWO POINTS
NUMBER LINE COORDINATE PLANE
PQ = | b – a | or | a – b |
Example Find the distance
between the two points -5 and 1.
The distance between d between two points with coordinates
(x2 - x1) and (y2 – y1) is given by
d = √ (x2 – x1)2 + (y2 – y1)2
Example Find the distance
between R(5.1) and S(-3,-3).
Midpoint of a Segment
Used for finding the coordinates of the midpoint of a segment in a coordinate plane.
If the endpoints are (x1,y1) & (x2,y2), then
2,
22121 yyxx
Ex: Find the midpoint of SP if S(-3,-5) & P(5,11
Ex: The midpoint of AB is M(2,4). One endpoint is A(-1,7). Find the coordinates of B.
)midpoint(2
,2
2121
yyxx
Independent Practice
Handout Homework Page 25-26 13-18 all; 23-28 all; 31 - 44
all Quiz next block on Sections 1-1 to 1-3 You must know the Distance and Midpoint
Formulas Study!!!!
1.4 ANGLE MEASURES
Geometry Online Textbook
User Name:GEOVA05
Password: crAju4re
Warm up
Practice
Angle symbol: 2 rays that share the same endpoint (or
initial point)
Y
Z
X
Sides – the rays XY & XZ
Vertex – the common endpoint; X
Named <YXZ, <ZXY (vertex is always in the middle), or <X (if it’s the only <X in the diagram).
Angles can also be named by a #. (<5)
5
There are 3 different <B’s in this diagram; therefore, none of them
should be called <B.
A
B
C
D<B ?
Angle Measurement
m<A means the “measure of <A”
Measure angles with a protractor.
Units of angle measurement are degrees (o).
Angles with the same measure are congruent angles.
If m<A = m<B, then <A <B.
Interior or Exterior?
B is ___________ C is ___________ D is ___________
in the interior
in the exterioron the <
A
B
C
D
Types of Angles Acute angle –
Right angle –
Obtuse angle –
Straight angle –
Measures between 0o & 90o
Measures exactly 90o
Measures between 90o & 180o
Measures exactly 180o
Ray Piece of a line with only one endpoint
(initial point) and continues forever in the other direction
Named by the endpoint and a second point named on the ray. (name MUST begin with the endpoint!)
AB
AB
Opposite Rays
2 rays that share a common initial point and face opposite directions.
QP and QS are opposite rays.P Q S
CONGRUENT ANGLES
Angles that have the same measure are congruent angles. Arcs on the figure also indicate which angles are congruent.
Practice
Example: 6 volunteers please!
Draw & label points A & B. Draw & label points C & D. Draw AB. Draw BC. Draw AC. Draw DA.
More Definitions Intersect –
2 or more figures intersect if they have one or more points in common.
Intersection – all points or sets of points the figures have in common
What is the intersection of:AB & DABC & ACBC & BC
WHEN 2 PLANES INTERSECT, THEIR INTERSECTION IS A
LINE.
Assignment