Geometry Math
Drawing Conjectures
Name __________________
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STATEMENT
CONCLUSION
A●
mABC  90o
●
B
C
●
Y
X
Z
Y is the midpoint of XZ
mQRS  90o
Q●
●
●
R
S
T●
X
●
U●
X is between U & T
ABC is isosceles with vertex
B
A
B
C
D
A
D
B
E
C
R
 RST is a right angle
T
S
B
AB  BC  AC
A
A
((
D
)
B
))
(
C
b
a
c
C
REASON
STATEMENT
CONCLUSION
REASON
A
ABC is equiangular
B
C
A
 BAC and  BCA are
complementary.
B
C
D
mABD  mBDC  mDCB
●
C
B
A
A
ABC is equilateral
B
C
mX  90o
X
mY  90o
Y
mZ  90o
Z
mN  90o
M
O
N
AB bisects XAM
mX  mY  90o
mA  mC  180o
ABC  XYZ
Definition of Congruent Angles
Y
XY  YZ  XZ
X
Z
A
B  C  A
B
C
STATEMENT
CONCLUSION
REASON
ABC is acute
Definition of an acute angle
XY  YZ
Definition of midpoint
QRS is obtuse
Definition of an obtuse angle
UX + XT = UT
Segment Addition Postulate
AB  BC
The two legs of an isosceles
triangle are congruent.
ABD  CDB
SSS
ABE  CBD
SAS
RST is a right triangle
Definition of a right triangle
ABC is a scalene triangle
Definition of a scalene triangle
ABD  CDB
ASA
a + b + c = 180o
Triangle Sum Theorem
The sum of the measures of the
3 angles of a triangle is 180o.
A●
mABC  90o
●
B
C
●
Y
X
Z
Y is the midpoint of XZ
mQRS  90o
Q●
●
●
R
S
T●
X
●
U●
X is between U & T
ABC is isosceles with vertex
B
A
B
C
D
A
D
B
E
C
R
 RST is a right angle
T
S
B
AB  BC  AC
A
A
((
D
)
B
))
(
C
C
b
a
c
STATEMENT
CONCLUSION
A
REASON
A  B  C
ABC is equiangular
ABC is equilateral
A
 BAC and  BCA are
complementary.
B
Definition of equiangular
triangle
All equiangular triangles are
equilateral
The acute angles of a right
triangle are complementary
C
D
mABD  mBDC  mDCB
The measure of an exterior
angle of a triangle equals the
sum of the remote interior
angles.
AB  BC  AC
Definition of equilateral triangle
ABC is equiangular
All equilateral triangles are
equiangular
XYZ is an acute triangle
Definition of an acute triangle
XYZ is an obtuse triangle
Definition of an obtuse triangle
AB bisects XAM
XAB  BAM
Definition of an angle bisector
mX  mY  90o
X and Y are
complementary angles
Definition of complementary
angles
A and C are
supplementary angles
Definition of supplementary
angles
mABC  mXYZ
Definition of Congruent Angles
XYZ is an equilateral
triangle
Definition of equiangular
triangle
XYZ is an equiangular
triangle
Definition of equilateral triangle
●
C
B
A
A
ABC is equilateral
B
C
mX  90o
X
mY  90o
Y
mZ  90o
Z
mN  90o
M
O
N
mA  mC  180o
ABC  XYZ
Y
XY  YZ  XZ
X
Z
A
B  C  A
B
C