geometry notes week 1. point:it has location and nothing else. no size. no height. no depth. no...
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Geometry NotesWeek 1
Point: It has location and nothing else. No size. No height. No depth. No friends.
Line:A straight, unbroken set of points that goes on forever. It has infinite length but no thickness.
A
B
AB BA
A
Plane: A surface with length and width but no thickness.
Notes –Vocabulary DAY1
AB BA
Line Segment: A line that has two endpoints.
AB
Ray: A line with ONE endpoint.
YB
A AB AY
Notes Vocabulary
Coplanar: On the same plane
Collinear: On the same lineF Z P
AB AC
A B A C
Ex:
A
B
C
2
2
1
What we CAN write:
AB AC
A B A C
What we CAN’T write:
AC BC
Equal=
NumbersAB
Congruent
AB
AB 2
A B 2
Shapes
DAY 2 - Congruency
A
B
C
D
FG
H
What do the markings indicate?What type of triangle has been formed?What are two statements of congruency that you can write from the quadrilateral?
Notes - Basic Angles
What We Can Write
EFD
DFE
F
Vertex: The common endpoint of the two rays of an angle.
D
F
E
1
1
What We Can’t Write
F
What We Can Write
CFE
EFC
EFD
DFE
1
2
D
F
E
C
1
2
CFD
DFC
Notes - Basic Angles
D
F
E
2. Notes - Basic Angles
D
F
E
2. Notes - Basic Angles
Angle Bisector: A ray that extends from the vertex of an angle and divides it into two congruent angles.
A
B
C
28°14°
14°
D
What We Can Write
AD is the angle bisector of BAC.
BAD DAC
Midpoint: The point on a segment that’s the same distance from both endpoints.
3
B CD
3D is the midpoint of BC
F
D
H
H is the midpoint of FD
D
E
A A is the midpoint of DE
DAY 3 - Midpoint
Midpoint Formula - How do we find the exact center of a line segment?
(7,8)
(3,2)
2. Notes - Midpoint FormulaHow do we find the exact center of a line segment?
x1 x22
,y1 y22
Conjecture 1: Midpoint Conjecture
If your points are and then your midpoint is:
x1,y1
x2,y2
(7,8)
(3,2)
x1 x22
,y1 y22
7 32,8 22
10
2,10
2
(5,5)
5,5
2. Notes - Midpoint FormulaLet’s make it work for us.
(-9,2)
(7,-6)
x1 x22
,y1 y22
9 72
,2 62
22, 42
(-1,-2)
-1,-2
2. Notes - Midpoint FormulaOne more time.