1.3 /1.5Segments and Angle Addition Postulate
California State Standards1. Understand and Use
undefined terms, axioms, theorems, and inductive and deductive reasoning
15. Use the Pythagorean Theorem17. Prove theorems using
coordinate geometry
Lesson GoalsUse the Segment Addition Postulate.Classify anglesUse the angle addition
postulate
ESLRs: Becoming Competent Learners, Complex Thinkers, and Effective Communicators
Basic Terms
Postulate (aka Axiom)
a rule that is accepted as true without proof
Theorem a rule that must be proven to be true.
This indicates that the points are collinear.
Postulate
Segment Addition PostulateIf B is between A and C then AB + BC = AC
A B C
AB BC
AC
The pieces of a segment add up to the whole segment.
example
Draw a sketch of the three collinear points, D, E, and F where D is between E and F. Write the Segment Addition Postulate for the 3 points.
E FD
ED DF EF
AB XYAB XY
Definition
Congruent Segments segments that have the same length
A B X Y
this representsa number equal to a number
this represents a figure the same size and
shape as another figure
the symbol for congruent
Definition
AngleTwo rays with a common initial point called
the vertexThe rays are called sides
BAC A oris the name of the angle
A
B
C
A is the vertex of the angle
the symbol for angle
angles can also be namedby a number placed in
the interior of the angle.
3
Interior
Exterior A
Definition
Interior of an angleThe points in the region between the sides
of the angle.
Exterior of an angleThe points in the region NOT between the sides
of an angle.
Definition
Congruent AnglesAngles that have the same measure
A
P
A P m A m P a number equal to a number figures the same size and shape
Definition
Adjacent AnglesTwo angles that have a common vertex and side, but have no common interior points.
Q
R
S
P
(angles that are next to each other)
common vertex
SummaryWhat is a postulate or axiom?
If point B is between A and C, then what do we know about the points? Write the segment addition postulate for the points.
When would the Distance Formula be used?
In mathematics you don’t understand things. You just get used to them.
– John von Neumann
Today’s Assignment
p. 21: 1 – 3, 11, 19, 20, 23 – 31 p. 30: 26 – 31, 39
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best effort.
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