Download sections 1.1-1.3

1.1­1.3 HNs Foundations of Geometry.notebook
September 19, 2016
Do Now #3
• Get a ruler, compass, and protractor
• Complete the chart, use properties learned in last class
Equation
3(5+2)­6(x+1)=21
Justification
given equation
1.1 Understanding Points, Lines, and Planes
Point ­ describes a location in space. No width, height, length, or size.
Line ­ a straight path with no thickness. It extends FOREVER.
Plane ­ flat surface with no thickness. Also extends FOREVER. UNDEFINED TERMS
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1.1­1.3 HNs Foundations of Geometry.notebook
September 19, 2016
How to label Points, Lines and Planes
Points that lie on the same line are called ________.
Points that lie on the same plane are called ________.
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1.1­1.3 HNs Foundations of Geometry.notebook
September 19, 2016
Segment ­ (or line segment) the part of a line consisting of two points and all the points
between them
Endpoint ­ a point at one end of a segment or the starting of a ray.
Ray ­ part of a line that starts at an endpoint and extends forever in one direction.
Opposite Rays ­ two rays that have a common endpoint and form a line.
How to label Segments, Endpoints, Rays and Opposite Rays
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1.1­1.3 HNs Foundations of Geometry.notebook
September 19, 2016
Use a sheet of paper as your plane. Use the pieces of
spaghetti to make
1 ­ a line
2 ­ a line segment
4 ­ a ray
5 ­ opposite rays
3 ­ a point
6 ­ an endpoint
MAKE SURE YOU LABEL ALL OF YOUR PIECES CORRECTLY!
Distance ­ l a­b l, or l b­a l
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1.1­1.3 HNs Foundations of Geometry.notebook
September 19, 2016
Distance formula : (x ­x ) + (y ­y )
L
M
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1.1­1.3 HNs Foundations of Geometry.notebook
September 19, 2016
Constructing Congruent Segments
Segment Addition Postulate
A
B
C
If B is between A and C, then AB + BC = AC
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1.1­1.3 HNs Foundations of Geometry.notebook
September 19, 2016
Do Now #4
1. Find the length of AC
A
9 cm B
C
16 cm
2. Find x. Then find the length of AB and BC.
A
B
3x cm
x+3 cm
C
23 cm
A
2x+3 cm
B
11 cm
C
28 cm
Midpoint ­ the point that bisects or divides the segment into two congruent segments
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1.1­1.3 HNs Foundations of Geometry.notebook
A
6x
B
September 19, 2016
3x+12
C
B is the midpoint of line segment AC.
Midpoint Formula: x +x y +y 2
2
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1.1­1.3 HNs Foundations of Geometry.notebook
September 19, 2016
N
M
1.3 Angles
Q
R
S
Angle ­ figure formed by two rays, or sides, with a common endpoint
Vertex
Interior of an angle
Exterior of an angle
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1.1­1.3 HNs Foundations of Geometry.notebook
September 19, 2016
Acute
Straight
Right
Obtuse
Constructing Congruent Angles and Angle Bisectors
angle bisector ­ a ray that divides an angle into two congruent angles
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1.1­1.3 HNs Foundations of Geometry.notebook
September 19, 2016
Angle Addition Postulate
P
C
A
B
m ABC = m ABP + m PBC P
C
A
100 degrees
15 degrees
B
What is the m ABP
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1.1­1.3 HNs Foundations of Geometry.notebook
September 19, 2016
P
C
A
m ABC = 102
B
m ABP = 5x m PBC = 2x­3
1 ­ Measure the angles on the handout, record answers on a
separate sheet of paper.
2 ­ Draw the following angles
36 degrees
156 degrees
3 ­ Book Work
87 degrees
pg. 9 #1, 3­6, 12, 32
pg. 17 #2­4,8,16
pg. 18 #24­26,31
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1.1­1.3 HNs Foundations of Geometry.notebook
September 19, 2016
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