Transcript Chapter 1: Tools of Geometry

Chapter 1: Tools of
Geometry
Lesson 1: Points, Lines and
Planes
Definitions
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Point- represents a location
Line- made up of points and has no thickness or
width, extends infinitely at both ends (cannot be
measured)
Collinear- points on the same line
Plane- flat surface made from points that has no
depth and extends in all directions infinitely
Coplanar- points or lines on the same plane
Space- boundless, 3-D set of all points that contains
lines and planes
Chapter 1 Foldable
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Step 1- fold the construction paper in half
both by width and length (hamburger and
hotdog)
Step 2- Unfold the paper and hold width wise,
fold in the ends until they meet at the center
crease
Step 3- Cut the folded flaps along the crease
so that there are now 4 flaps
Upper Left flap- Lesson 1.1
Points, Lines and Planes
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Label the outside of the flap with the lesson
number and title.
Inside the flap create a grid with 7 columns
and 4 rows.
Copy the notes into the foldable, then draw and label your
own examples based on the information in the chart.
Name
Model
Point
Drawn
Named By
Facts
As a dot
A capitol
letter
A point has
neither size
nor shape
P
Line
n
B
With an
arrowhead
at both ends
A
Plane
Y
Z
X
S
As a
shaded,
slanted, 4sided figure
Two letters
representing
points on
the line- or
the script
letter
There is
exactly 1
line through
any two
points
A capital
script letter
or by any
three letters
of noncollinear
points
There is
exactly 1
plane
through any
three noncollinear
points
Words/
Symbols
point P
line n
line AB
line BA
plane S
plane XYZ
plane XZY
plane ZXY
plane ZYX
plane YXZ
plane YZX
Examples
A. Use the figure to name a line containing point K.
B. Use the figure to name a plane containing point L.
C. Use the figure to name the plane two different ways.
A. Name the geometric shape modeled by a 10  12 patio.
B. Name the geometric shape modeled by a water glass on
a table.
C. Name the geometric shape modeled by a colored dot on
a map used to mark the location of a city.
D. Name the geometric shape modeled by the ceiling of
your classroom.
A. How many planes appear in this figure?
B. Name three points that are collinear.
C. Are points A, B, C, and D coplanar? Explain.
Chapter 1: Tools of
Geometry
1.2 Linear Measure
Definitions
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Line segment- part of a line that has two
endpoints and can be measured(named by
the letters marking the endpoints)
Congruent- same shape and size (segments
that have the same measure)
A. Find LM.
B. Find XZ.
C. Find x and ST if T is between S and U, ST = 7x, SU = 45,
and TU = 5x – 3.
Find SE.
Find a if AB = 4a + 10, BC
= 3a – 5, and AC = 19.
Chapter 1: Tools of
Geometry
Lesson 3: Distance and Midpoint
Definitions
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Midpoint- the point on a segment that divides
the segment into two congruent segments
Segment bisector- any line, segment or plane
that intersects a segment at its midpoint
Distance and Midpoint
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Distance Formula- used
to find the length of a
segment.
d  ( x2  x1 ) 2  ( y2  y1 ) 2
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Midpoint Formula- used
to find the point half
way down a segment
 x1  x2 y1  y2 
M
,

2 
 2
ex: Find the distance between
A (5,1) and B (-3, -3).
ex: Find the midpoint of JK if
J(-1,2) and K(6, 1)
*on a number line- subtract the
endpoint values
* on a number line- add the
endpoint values and divide by 2
Use the number line to find the midpoint and the measure
of AX.
Find the midpoint and distance between
E(–4, 1) and F(3, –1).
Find the distance
and midpoint of AM
Find the coordinates of R if N (8, –3) is the midpoint
of RS and S has coordinates (–1, 5).
Find LM. Assume that the figure is not drawn to
scale.
Find the value of x and ST if T is between S and U, ST = 7x,
SU = 45, and TU = 5x – 3.
Find the value of n and WX if W is
between X and Y, WX = 6n – 10, XY = 17,
and WY = 3n.
Chapter 1: Tools of
Geometry
Lesson 4: Angle Measure
Definitions
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Degree- the unit of measurement for an angle
Ray- a part of a line which has one endpoint and one end that
extends infinitely (name with the endpoint first and then any
other point on the ray)
Opposite rays- two rays that share an endpoint and extend in
opposite directions (together they make a line)
Angle- formed by two non-collinear rays that have a common
endpoint
Sides of an angle- rays
Vertex- the common endpoint of the rays of an angle
Angle Bisector- a ray or line that divides an angle into two
congruent angles
Naming and Classifying
Angles
A
Angle:
B
4
C
-B is the vertex
-ray BA and ray BC are the
sides( BA and BC )
-Angle names:
ABC, CBA
 B,  4
-Angle bisector : makes 2
congruent angles
Name
Measure
Right
Angle
90
Acute
Angle
Less than
90
(0 < x < 90)
Obtuse Between
Angle 90 and
180
(90 < x < 180)
Model
A. Name all angles that have
B as a vertex.
B. Name the sides of 5.
C.
A. Measure TYV and classify it as right, acute, or
obtuse.
B. Ray YT bisects angle SYU. Angle TYS = 2x-24,
angle UYT = x+16.
Find x and the measure of angle SYU.
Chapter 1: Tools of
Geometry
Lesson 5: Angle Relationships
Definitions
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Adjacent angles: two angles that lie in the same plane, have a
common vertex and a common side, but no common interior
points
Vertical angles: two nonadjacent angles formed by two
intersecting lines
Linear pair: a pair of adjacent angles with non-common sides that
are opposite rays
Complementary angles: two angles with measures that add up to
90
Supplementary angles: two angels with measures that add up to
180
Perpendicular (  ): lines, segments or rays that form right
angles
Angle Relationship examples
Adjacent angles
M
Vertical angles
O
L
C
B
N
D
Linear pair
D
A
E
Complementary angles
B
A
72
18
C
Supplementary angles
Perpendicular lines
R
40
140
S
V
T
U
A. Name two adjacent angles
whose sum is less than 90.
B. Name two acute vertical angles.
Find the measures of two supplementary
angles if the measure of one angle is 6 less
than five times the measure of the other
angle.
A. Name an angle supplementary
to BEC.
B. Name a linear pair whose
vertex is E.
C. Name two acute vertical
angles.
Find the measures of two complementary
angles if one angle measures six degrees
less than five times the measure of the
other.
The supplement of A measures 140
degrees. What is the measure of the
complement of A?
ALGEBRA Find x and y so that
KO and HM are perpendicular.