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

example

AB

CD

E

CD DE

35AE

Find DE

9AC

9 35x x

AC CD DE AE

x

9

35

x

13x

2 9 35x

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.

G

D

FC

E

You Try

Name the indicated angle

G

D

FC

E

You Try

Name a point in the interior of the angle.

E

G

D

FC

E

You Try

Name a point in the exterior of the angle.

G

G

D

FC

E

You Try

Name the indicated angle.

or GDF FDG

or GDC CDG

example

Name the indicated angle

G

D

FC

E

Definition

Angle MeasurementThe number of degrees in an arc between the sides of an angle.

A

B

C

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

then m CAP

Postulate

Angle Addition Postulate

AP

m PAB m CAB

C

B

Example

C

E F

D

Example

A

BC

G

120o

35o

xo

m ABG m GBC m ABC

35 120x

85x

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

You Try

Name all the pairs of adjacent angles.

D

AB

C

E

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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