Find every  measure you can
TA IA, TR  RN
mTRI=120
T
N
R
I
A
K
J
M
L
P
Find every  measure you can
PLM  MJK
mKLM=88
mLPM  mPKJ  28
J
Find every  measure you can
I
SA KY , JA  AK , JY  YE
KY  YE , KY JE
S
A
Y
K
E
Find the angle made by the rays which bisect the base angles of an isosceles triangle with a
vertex angle of 108
A
BF bisects EBC
B
CF bisects ECB
E
D
ABCD is a trapezoid with bases AB & CD
mABE=32
mECD=28
Find mBEC & mBFC
F
C
A
D is the midpoint of AB
E is the midpoint of AC
BE bisects ABC
AE  BE
Determine all s
D
B
E
C
Prove: If the bisector of an angle of a triangle passes through the midpoint of its opposite side,
it is also perpendicular to that side.
AC  CE
A
BF  AE
mCEG  140
B is the midpoint of AC
D is the midpoint of CE
Find every angle that you can
F
B
C
D
E
G
A
VIP ( Very Important Problem)
AD  CD  CB
AC  AB
Find mA
D
B
C
Prove: If the bisector of an angle of a triangle is a median of the triangle, then it is also an
altitude of the triangle.
E
Find the sum of the measures of the
interior angles of PENTA
N
That is find
mP  mE  mN  mT  mA
P
T
A
Prove or disprove: If two triangles are isosceles, then ASS determines congruence
A, B , C  m
D
Given: DCm
DAC  DBC
Prove: CABCBA
m
C
STATEMENTS
A
B
























REASONS
P
R
O
D
B
Given :
PO  OB
PDO  BRO
ODB  OBD
Prove: PR RB
Given :
EF AH
A
F
AE EH
Prove:
AFEH
E
H
Given:
Prove:
B  C
ADB  AEC
A
E
D
F
B
C
Q
Given: P  R
QMN  QNM
Prove: PM
 EN
P
M
N
R
Given: ALGAGL,
A
AL& AG trisect NAE,
E  N
Prove: EL  NG
E
H
L
G
The measure of one interior angle of a regular polygon is 165. Find the number of sides of the
polygon.
Two consecutive angles of a hexagon are right angles, The remaining four angles are
congruent. Find the measure of the non right angles of the hexagon.
If a polygon has 328454 diagonals, how many sides does it have?
Problems 1-6 are about a convex polygon has 24 sides.
1. What is the sum of the interior angles?
2. If it is regular, what is the measure of one interior angle?
3. What is the sum of the exterior angles?
4. If it is equiangular, what is the measure of one exterior angle?
5. How many diagonals can be drawn from one vertex?
6. How many diagonals does it have altogether?
The remaining questions apply to a regular polygon with n sides.
7. If one exterior angle measures 8, find n
8 If one interior angle measures 168, find n
9. Find the measure of one interior angle of a regular decagon
10. If the sum of the measures of the interior angles measures 10440, what is the measure of
one interior angle?
Some REGULAR POLYGON Numbers
# of sides
# of diagonals
sum of interior s
Sum of exterior s
Each interior 
Each exterior 
10
20
35
1440
360
144
36
12
170
360
360
44
2
ABCDE is a regular pentagon. Draw BE & BD .
Find mAEB, mDBC, mEBD, mBED and mBDE
THEN, draw EC
Label the point of intersection of CE and BD as point P.
Find mEPD
C
O
OCTAGNPB is a regular octagon with three of its
diagonals drawn.
How many diagonals are not drawn?
T
A
B
G
P
N
Determine mOCB
mBCP
mPCN
mCPN
bg b g
bg
Quadrilateral ABOX has vertices A at 6,4 , B at 0,10 , O at the origin and X at 2,0 . Find
the measures of the interior angles of ABOX
BC  CD  DE
A
BA CD
mDCE  70
D
B
C
Find all other s in the 
E
Given: O
mPST=20
mSTF=50
Find mTPS and mTFS
P
T
S
O
F
ABCDEF is a regular hexagon
Find
mAGB
mBHG
mBED
B
A
G
H
F
C
E
D
ABCDEF is a regular hexagon. Find the measures of each of the following angles
1. ABF
2. ABE
3. FBE
STW is equilateral
SKWT ,WR ST
S
Find
mKST
mSMR
mTWR
mMWS
R
M
W
K
T
The median to the hypotenuse of ABC is congruent to one of the legs. Find all angles
including the ones formed by the median.
Given : AMB  ABW
B
Prove: ABM  W
A
M
W