Download Equidistant Angle Bisector Theorem: P is on the bisector of ∠ABC, if

Equidistant Angle Bisector
Theorem:
P is on the bisector of ∠ABC,
if and only if
P is equidistant to each side, AP
= PC.
Perpendicular Bisector
Theorem:
P is on the⊥ bisector of AB
if and only if
P is equidistant to A & B.
AP = PB
l
A
M
A
P
D
B
P
B
INEQUALITIES IN ONE ∆
Exterior Angle Inequality
m∠4 > m∠1 & m∠4 > m∠2
1
2
3
C
∆ Inequality
a+b>c
b+c>a
c+a>b
⇓
|a - b| < c < a + b
c
a
B
Opposites Inequality
m∠A > m∠B > m∠C ⇔ BC > CA > AB
The larger angles are opposite the larger sides in a ∆.
T
INEQUALITIES IN TWO ∆’s
C
Y
Z
4
A
b
B
C
Triangle Midsegment Theorem
If IM = MT & ID = DR,
I
then
① MD = 1 TR.
M
D
2
➁ MD//TR.
R
A
X
SAS ∆ Inequality
If AB = XY and AC = XZ and m∠A < m∠X,
then BC < YZ.
SSS ∆ Inequality
If AB = XY and AC = XZ and BC < YZ,
then m∠A < m∠X.
Midsegment Corollary
The joined midpoints of
consecutive sides of any
quadrilateral form a parallelogram.