segment addition postulate if three points, a, b, and c, are collinear, and point b...
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Segment Addition Postulate.If three points, A, B, and C, are
collinear, and point B is between points A and C, then
AB + BC = AC
Segment Addition Postulate.If three points, A, B, and C, are
collinear, and point B is between points A and C, then
AB + BC = AC
A B C
Segment Addition Postulate.If three points, A, B, and C, are
collinear, and point B is between points A and C, then
AB + BC = AC
A B C
Segment Addition Postulate.If three points, A, B, and C, are
collinear, and point B is between points A and C, then
AB + BC = AC
A B C
Angle Addition Postulate.If three rays, AB, AC, and AD share a common endpoint, A, such that AC is
in the interior of , then
Angle Addition Postulate.If three rays, AB, AC, and AD share a common endpoint, A, such that AC is
in the interior of , then
A
BC
•
••
D
Angle Addition Postulate.If three rays, AB, AC, and AD share a common endpoint, A, such that AC is
in the interior of , then
A
BC
•
••
D
Angle Addition Postulate.If three rays, AB, AC, and AD share a common endpoint, A, such that AC is
in the interior of , then
A
BC
•
••
D
Angle Addition Postulate.If three rays, AB, AC, and AD share a common endpoint, A, such that AC is
in the interior of , then
A
BC
•
••
D
Theorem 8: If a segment is added to two congruent segments, the sums are
congruent. (Addition property)
Theorem 8: If a segment is added to two congruent segments, the sums are
congruent. (Addition property)
A B C D
Theorem 8: If a segment is added to two congruent segments, the sums are
congruent. (Addition property)
A B C D
Theorem 8: If a segment is added to two congruent segments, the sums are
congruent. (Addition property)
A B C D
Theorem 8: If a segment is added to two congruent segments, the sums are
congruent. (Addition property)
A B C D
Theorem 8: If a segment is added to two congruent segments, the sums are
congruent. (Addition property)
A B C DGiven: Prove:
Theorem 8: If a segment is added to two congruent segments, the sums are congruent. (Addition
property)
A B C DGiven: Prove:
Theorem 8: If a segment is added to two congruent segments, the sums are congruent. (Addition
property)
A B C DGiven: Prove:
Theorem 8: If a segment is added to two congruent segments, the sums are congruent. (Addition
property)
A B C DGiven: Prove:
Theorem 8: If a segment is added to two congruent segments, the sums are congruent. (Addition
property)
A B C DGiven: Prove:
Theorem 9: If an angle is added to two congruent angles, the sums are
congruent. (Addition property)
Theorem 9: If an angle is added to two congruent angles, the sums are
congruent. (Addition property)
1 23
• ••
•
A BC
DF
Given:
Prove:
Theorem 9: If an angle is added to two congruent angles, the sums are
congruent. (Addition property)
1 23
• ••
•
A BC
DF
Given:
Prove:
Theorem 10: If congruent segments are added to congruent segments,
the sums are congruent. (Addition property)
Theorem 10: If congruent segments are added to congruent segments,
the sums are congruent. (Addition property)
•
•AB
C X
Y
Z
Theorem 10: If congruent segments are added to congruent segments,
the sums are congruent. (Addition property)
•
•ABC X
Y
Z∂
Theorem 10: If congruent segments are added to congruent segments,
the sums are congruent. (Addition property)
•
•ABC X
Y
Z∂
Given:
Theorem 10: If congruent segments are added to congruent segments,
the sums are congruent. (Addition property)
•
•ABC X
Y
Z
Given:
Prove:
Theorem 11: If congruent angles are added to congruent angles, the sums are congruent. (Addition property)
1
3
Theorem 11: If congruent angles are added to congruent angles, the sums are congruent. (Addition property)
12
34
Theorem 11: If congruent angles are added to congruent angles, the sums are congruent. (Addition property)
12
34
Given:
Theorem 11: If congruent angles are added to congruent angles, the sums are congruent. (Addition property)
•
•
•
•
A
B C
X
YZ
12
34
Given:
Prove:
Theorem 12: If a segment (or angle) is subtracted from congruent segments
(or angles), the differences are congruent. (Subtraction property)
Theorem 12: If a segment (or angle) is subtracted from congruent segments
(or angles), the differences are congruent. (Subtraction property)
A B C D
Given: Prove:
Theorem 12: If a segment (or angle) is subtracted from congruent segments
(or angles), the differences are congruent. (Subtraction property)
A B C D
Given: Prove:
Theorem 12: If a segment (or angle) is subtracted from congruent segments
(or angles), the differences are congruent. (Subtraction property)
A B C D
Given: Prove:
Theorem 12: If a segment (or angle) is subtracted from congruent segments
(or angles), the differences are congruent. (Subtraction property)
1 23
• ••
•
A BC
DF
Given:
Prove:
Theorem 12: If a segment (or angle) is subtracted from congruent segments
(or angles), the differences are congruent. (Subtraction property)
1 23
• ••
•
A BC
DF
Given:
Prove:
Theorem 13: If congruent segments (or angles) are subtracted from congruent
segments (or angles), the differences are congruent. (Subtraction property)
Theorem 13: If congruent segments (or angles) are subtracted from congruent
segments (or angles), the differences are congruent. (Subtraction property)
•
•ABC X
Y
Z
Given:
Prove:
Theorem 13: If congruent segments (or angles) are subtracted from congruent
segments (or angles), the differences are congruent. (Subtraction property)
•
•ABC X
Y
Z
Given:
Prove:
Theorem 13: If congruent segments (or angles) are subtracted from congruent
segments (or angles), the differences are congruent. (Subtraction property)
•
•ABC X
Y
Z
Given:
Prove:
Theorem 13: If congruent segments (or angles) are subtracted from congruent segments (or
angles), the differences are congruent. (Subtraction property)
•
•
•
•
A
B C
X
YZ
12
3
4
Given:
Prove:
Theorem 13: If congruent segments (or angles) are subtracted from congruent segments (or
angles), the differences are congruent. (Subtraction property)
•
•
•
•
A
B C
X
YZ
12
3
4
Given:
Prove:
Theorem 13: If congruent segments (or angles) are subtracted from congruent segments (or
angles), the differences are congruent. (Subtraction property)
•
•
•
•
A
B C
X
YZ
12
3
4
Given:
Prove:
A B C D
Given:
Conclude:
A B C D
Given:
Conclude:
A B C D
Given:
Conclude:
A B C D
Given:
Conclude:
A B C DGiven:
Conclude:
66
A B C DGiven:
Conclude:
66
A B C DGiven:
Conclude:
66 4
A B C DGiven:
Conclude:
66 4
A B C DGiven:
Conclude:
9
A B C DGiven:
Conclude:
9
A B C DGiven:
Conclude:
9 1212
A B C DGiven:
Conclude:
9 1212
1 23
• ••
•
A BC
DF
Given: Conclude:
1 23
• ••
•
A BC
DF
Given: Conclude:
23
1
• ••
•
A BC
DF
Given: Conclude:
1 23
• ••
•
A BC
DF
Given: Conclude:
1 23
• ••
•
A BC
DF
Given: Conclude:
1 23
• ••
•
A BC
DF
Given: Conclude:
12
3
• ••
•
A BC
DFGiven: Conclude:
12
3
• ••
•
A BC
DFGiven: Conclude:
40º 20º
12
3
• ••
•
A BC
DFGiven: Conclude:
40º
40º 20º
12
3
• ••
•
A BC
DFGiven: Conclude:
40º
40º 20º
12
3
• ••
•
A BC
DFGiven: Conclude:
40º
40º 20º
12
3
• ••
•
A BC
DFGiven: Conclude:
40º
40º 20º
•
•
L
SC
Given:
Conclude:2
1
3
•
•B
A
•
•
L
SC
Given:
Conclude:2
1
3
•
•B
A
•
•
L
SC
Given:
Conclude:2
1
3
•
•B
A
•
•
L
SC
Given:
Conclude:2
1
3
•
•B
A
•
•
L
SC
Given:
Conclude:2
1
3
•
•B
A20º
20º
•
•
L
SC
Given:
Conclude:2
1
3
•
•B
A20º
20º
50º
Theorem 8: If a segment is added to two congruent segments, the sums are congruent. (Addition
property)
Theorem 8: If a segment is added to two congruent segments, the sums are congruent. (Addition
property)
Theorem 9: If an angle is added to two congruent angles, the sums are congruent. (Addition property)
Theorem 8: If a segment is added to two congruent segments, the sums are congruent. (Addition
property)
Theorem 9: If an angle is added to two congruent angles, the sums are congruent. (Addition property)
Theorem 10: If congruent segments are added to congruent segments, the sums are congruent.
(Addition property)
Theorem 8: If a segment is added to two congruent segments, the sums are congruent. (Addition
property)
Theorem 9: If an angle is added to two congruent angles, the sums are congruent. (Addition property)
Theorem 10: If congruent segments are added to congruent segments, the sums are congruent.
(Addition property)
Theorem 11: If congruent angles are added to congruent angles, the sums are congruent. (Addition
property)
Theorem 12: If a segment (or angle) is subtracted from congruent segments (or angles), the differences
are congruent. (Subtraction property)
Theorem 12: If a segment (or angle) is subtracted from congruent segments (or angles), the differences
are congruent. (Subtraction property)
Theorem 13: If congruent segments (or angles) are subtracted from congruent segments (or angles), the
differences are congruent. (Subtraction property)