Segment Addition Postulate If three points, A, B, and C, are collinear, and point B...
Transcript of Segment Addition Postulate If three points, A, B, and C, are collinear, and point B...
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)