GEOMETRY
Special Bisectors in
≅
∆
’s
NAME_________________________
Triangles
DATE __________
Per.___________
∆ ∠ BISECTOR THM.:
If two triangles are congruent, then their corresponding
angle bisectors
are congruent.
4.
C
N
G
T
I
A
O
R
Angle Bisector Theorem
Corresponding Parts
Substitution & Transitive Properties
Angle-Side-Angle Postulate
Definition of Angle Bisector
GIVEN: ∆CON ≅ ∆TRI;
and
&
3.
Fill in the
PROVE
statement above. Then make a flow-chart proof out of the boxes shown.
PROVE:
≅
Definition of
∠ Congruence
∆ ⊥ BISECTOR THEOREM:
If two triangles are congruent, then their corresponding
⊥ bisectors
are congruent.
P
E
R
N
D
I
A
U
C
L
C.P.C.T.C.
Midpoint Theorem
Substitution & Transitive Properties
Perpendicular Definition
Definition of Right
∆
’s
Leg-Angle Theorem
RN =PR ÷2; CU =IU ÷2
RN ≅UC
∠DNR & ∠LCU are right angles
Right Triangles ∆DRN, ∆LUC
∆DRN ≅ ∆LUC
ND ≅CL
GIVEN: ≅
and
&
PROVE:
≅
Definition of Congruent
∆
’s
∠CON ≅ ∠TRI; ∠N≅ ∠I; NO ≅IR
m∠NOG =m∠CON ÷2; m∠IRA =m∠IRT ÷2;
m∠NOG =m∠IRA
∠NOG ≅ ∠IRA
∆GON ≅ ∆ARI
OG ≅RA
Using the boxes above, write a paragraph proof of the Triangle Perpendicular Bisector Theorem.
∠R≅ ∠U;PR ≅IU
∠CON ≅ ∠TRI; ∠N≅ ∠I; NO ≅IR
Definition of Congruent
∆
’s
Definition of Angle Bisector
∠COG ≅ ∠NOG; ∠ART ≅ ∠ARI
∠COG ≅ ∠NOG; ∠ART ≅ ∠ARI
m∠NOG =m∠CON ÷2;
m∠IRA =m∠IRT ÷2;
Angle Bisector Theorem
Substitution & Transitive Properties
∠NOG ≅ ∠IRA
m∠NOG =m∠IRA
Definition of
∠ Congruence
OG ≅RA
Corresponding Parts
∆GON ≅ ∆ARI
Angle-Side-Angle Postulate
∠R≅ ∠U;PR ≅IU
C.P.C.T.C.
Definition of
≅
Triangles
RN =PR ÷2; CU =IU ÷2
Midpoint Theorem
Perpendicular Definition
∠DNR & ∠LCU are right angles
∆DRN ≅ ∆LUC
Leg-Angle Theorem
Right Triangles ∆DRN, ∆LUC
Definition of Right
∆
’s
ND ≅CL
Substitution & Transitive Properties
RN ≅UC
Definition of
≅
Triangles
