unit 1.3a segment addition postulate amp midpoint theorem cp
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8/10/2019 Unit 1.3a Segment Addition Postulate Amp Midpoint Theorem CP
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Unit 1.3 - Segment and angle relationships1.3a Prove theorems involving the Segment Addition Postulate
1.3b Formal geometric constructions using a variety of tools and
methods to copy and bisect an angle
1.3c Prove theorems involving the Angle addition postulate
1.3d Prove theorems about angle pairs
1.3e Prove theorems involving parallel lines and transversals
1.3f Formal geometric constructions using a variety of tools andmethods to construct perpendicular lines.
Common Core State Standards for Mathematical Content Congruence G-CO
Prove geometric theorems[Focus on validity of underlying reasoning while using variety of ways of writing proofs]G-CO.9Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a
transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent;
points on a perpendicular bisector of a line segment are exactly those equidistant from the segments endpoints.
G-CO.12Make formal geometric constructions with a variety of tools and methods (compass and straightedge,
string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle;
bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a
line segment; and constructing a line parallel to a given line through a point not on the line.
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1.3a Prove theorems involving the
Segment Addition Postulate
Postulate: Mathematical statement thatis accepted without proof
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Segment Addition Postulate
If B is between A and C, then
AB + BC = AC.
A BC
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Write a mathematic equation for FA using the
segment addition postulate.
What would the equation look like now?
FA =
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1. If N is between M and P and
MN = 10, MP = 25, find NP
10
25
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A flight from PVD to NYC is 143 miles
A flight from PVD to Washington DC is 355 miles
A flight from NY to Washington DC is _____ miles
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Seg. Add. Post. Example
If J is between H and K and HJ=5x-3 , JK = 4x,
HK = 8x, find HJ, JK, HK
Ans: Draw a diagram
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Example
M is between L and N. Find eachmeasurement if: LM = 4x+6 ,
LN = 5x+10
MN = 3x
4
4
82
10527
1054364
x
x
xx
xxx
LM + MN = LN
LM =4(4)+6 = 22
MN = 3(4)-4 = 8
LN = 5(4)+10 = 30
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If U is between T and B, find the value of x
and the measure of if
TU= 4x1, UB = 2x -1, and TB = 5x
Explain all your work
TU
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Ex: if DE=2, EF=5, and DE=FG,
find FG, DF, DG, & EG.
DE
F G
FG=2
DF=7
DG=9
EG=7
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Write an expression for QR
13x + 25
8x+5
PR = PQ + QR13x + 25 = (8x+5) + QR
-8x-8x
5x + 25 = 5 + QR-5-5
5x + 20 = QR
QR =5x + 20
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Segment bisectors
M is the midpoint of AB
MBAM
Segment AM is CONGRUENTto segment MB
Congruent segments: Segments that have the
same length
and AM = MB
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M is the midpoint of . Find AM and MBAB
26
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If M is the midpoint of ,
AM = 2x + 11, MB = 4x
5
Find the value of x and the measure of
AB
AB
2x + 11 4x - 5
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CP Geometry
Assignment
In class assignment: Practice worksheet 1.3aSegment addition postulate & midpoint
theorem
Homework: Page 33: 22-25, 38-40,
Page 41: 15-23, 33-35
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