Transcript Chapter 1: Tools of Geometry
Chapter 1: Tools of Geometry
Lesson 1: Points, Lines and Planes
Definitions
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
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
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 Drawn Named By Facts Words/ Symbols Examples Point
As a dot A capitol letter A point has neither size nor shape point P P
Line Plane
A Y Z
S
X
n
B With an arrowhead at both ends Two letters representing points on the line- or the script letter There is exactly 1 line through any two points line
n
line AB line BA As a shaded, slanted, 4 sided figure A capital script letter or by any three letters of non collinear points There is exactly 1 plane through any three non collinear points plane
S
plane XYZ plane XZY plane ZXY plane ZYX plane YXZ plane YZX
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
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
= 3
a
if
AB
= 4
a
– 5, and
AC
+ 10, = 19.
BC
Chapter 1: Tools of Geometry
Lesson 3: Distance and Midpoint
Definitions
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
Distance Formula- used to find the length of a segment.
d
(
x
2
x
1 ) 2 (
y
2
y
1 ) 2
ex: Find the distance between A (5,1) and B (-3, -3).
Midpoint Formula- used to find the point half way down a segment
M x
1 2
x
2 ,
y
1 2
y
2
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 of RS and S has coordinates
(8, –3)
is the midpoint
( –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
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: Name Right Angle Measure 90 4 B C -B is the vertex -ray BA and ray BC are the sides( BA and BC ) -Angle names: ABC, CBA -Angle bisector : makes 2 congruent angles Acute Angle Obtuse Angle Less than 90 (0 < x < 90) Between 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 obtuse
.
and classify it as
right, acute,
or 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
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 angles
Angle Relationship examples
Adjacent angles M O L Linear pair B A N D C Supplementary angles 40 140 Vertical angles D A C B E Complementary angles 72 18 Perpendicular lines R S V U T
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.