Download Geometry Proofs Booklet

1
GEOMETRY – ADVANCED
Proofs Code
Name: ___________________
Period: ______
Point B is between
A and C
C
B
If a point is a on a segment, the
segment is separated into two
smaller parts which add up to
equal the whole segment
A
Segment
Addition
Postulate
AB + BC = AC
E is the Midpoint of FD
D
E
F
BD is in the
interior
of ∠ABC
E
Midpoint
Theorem
FE ≅ ED
If a segment has a midpoint, then
it is divided into 2 congruent
segments.
D
F
D
A
B
C
Angle Addition
Postulate
m∠ABD + m∠DBC = m∠ABC
If 2 small angles share a ray, then
they can be added together to get
one large angle
2
AB ≅ CD
B
D
A
If 2 segments are congruent, then
they have equal measures.
C
Definition of
Congruent
Segments
AB = CD
∠1 and ∠2
are complementary
1
2
Definition of
Complementary
Angles
m∠1 + m∠2 = 90
If 2 angles are complementary,
then their measures have a sum
of 90 degrees.
∠3 and ∠4
are supplementary
3
m∠3 + m∠4 = 180
4
Definition of
Supplementary
Angles
If 2 angles are complementary,
then their measures have a sum
of 180 degrees.
∠5 and ∠6 are
Vertical Angles
5
6
If 2 are vertical angles, then they
are congruent.
∠5 ≅ ∠6
Vertical Angles
Are Congruent
3
∠3 and ∠4 are
In a Linear Pair
3
If two angles are in a linear pair,
then the sums of their measures
is 180
4
Sum of Angles
in a Linear Pair
Equals 180
m∠3 + m∠4 = 180
E is the Midpoint
of FD
D
E
A midpoint divides a segment
into two equal parts.
F
FE = ED
Definition of
Midpoint
Line l is a
Segment Bisector
B
M
l
A
Definition of
Segment
Bisector
If a segment, line, or a plane is a
segment bisector then it
intersects the segment at its
midpoint.
M is a Midpoint
∠1 ≅ ∠2
2
1
If two angles are congruent, then
they have equal measures.
m∠1 = m∠2
Definition of
Congruent
Angles
4
BD is an
Angle Bisector
D
A
B
C
If a ray bisects an angle, it creates
two congruent angles.
Definition of
Congruent
Angles
∠ABD ≅ ∠DBC
∠T is a
Right Angle
T
If an angle is a right angle, then it
measures 90 degrees.
Definition of
Right
Angles
m∠T = 90
ST ⊥ TW
S
W
T
∠STW is
a right angle
Definition of
Perpendicular
Lines
If two lines are perpendicular
(symbol ⊥ )
Then the four angles formed are
right angles.
∠1 and ∠2 are
Right angles
2
1
∠1 ≅ ∠2
All Right Angles
are Congruent
If two angles are right angles,
then they are congruent.
5
∠1 is complementary
to ∠2
∠3 is complementary
to ∠2
1
2
3
∠1 ≅ ∠3
2 Angles are
complementary to
the same angle are
congruent
∠1 is supplementary
to ∠2
∠3 is supplementary
to ∠2
∠1 ≅ ∠3
If two angles are supplementary
to the same angle (or congruent
angles), then they are congruent
to each other.
2
3
1
2 Angles are
supplementary to
the same angle are
congruent
If two angles are supplementary
to the same angle (or congruent
angles), then they are congruent
to each other.
∠1 and ∠2
Are a linear pair
1
∠1 and ∠2
Are supplementary
2
If two angles are in a linear pair,
then they are supplementary
angles.
Supplements
Theorem
*2 angles in a linear pair are
supplementary angles*