5-1Per pendicular s and Bisector s
( one of t hese t wo pr oof s wi l l be on t he t est )
Per pendicular Bisector Theor em:
I f a poi nt i s on t he per pendi cul ar bi sect or of a segment , t hen i t
i s equi di st ant f r om t he endpoi nt s of t he segment
Statements
Reasons
Given:
Pr ove:
Conver se of the Per pendicular Bisector Theor em:
I f a poi nt i s equi di st ant f r om t he endpoi nt s of a segment , t hen
i t i s on t he per pendi cul ar bi sect or of a segment .
Angle Bisector Theor em
I f a poi nt i s on t he bi sect or of an angl e, t hen i t i s equi di st ant
f r om t he si des of t he angl e.
Statements
Reasons
Given:
Pr ove:
Conver se of the Angle Bisector Theor em:
I f a poi nt i s equi di st ant f r om t he si des of an angl e, t hen i t i s
on t he bi sect or of an angl e.
My Tr iangle Center s Summar y
Tr iangle Center
Point of Concur r ency
Fun Fact
5.5 Inequalities in One Tr iangle
Theor em 5.10
I f one si de of a t r i angl e i s l onger t han anot her si de, t hen t he
angl e opposi t e t he l onger si de i s l ar ger t han t he angl e opposi t e
t he shor t er si de.
Theor em 5.11
I f one angl e of a t r i angl e i s l ar ger t han anot her angl e, t hen t he
si de opposi t e of t he l ar ger angl e i s l onger t han t he si de
opposi t e t he smal l er angl e.
Exter ior Angle Inequality Theor em
The measur e of an ext er i or angl e of a
t r i angl e i s gr eat er t han t he measur e of ei t her
of t he t wo non- adj acent i nt er i or angl es.
Di agr am:
Tr iangle Inequality Theor em
The sum of t he l engt hs of any t wo si des of a t r i angl e Di agr am:
i s gr eat er t han t he l engt h of t he t hi r d si de.
AB + BC > AC
BC + AC > AB
AC + AB > BC
5.4 Midsegment Theor em
Diagr am:
midsegment of a tr iangle
Definition: a segment that
connects the midpoints of two
sides of a tr iangle
Theor em 5.9: The Midsegment Theor em
The segment connecting the two sides of a tr iangle is par allel to the thir d side and half as
long.
Coor dinate Pr oof: Par allel
Coor dinate Pr oof: Half as Long