2. Given: A is the midpoint of MT, A is the
midpoint of SR.
Prove: MS ║TR.
Statements:
1. A is the midpoint of MT, A
is the midpoint of SR.
2. MA ≅ TA, SA ≅ RA
3. ∠MAS ≅ ∠TAR
4. ∆MAS ≅ ∆TAR
5. ∠M ≅ ∠T
6. MS ║ TR
Reasons:
1. Given
A
M
T
R
S
3. Given: A is the midpoint of MT, A is the
midpoint of SR.
Prove: MS ║TR.
Statements:
1. A is the midpoint of MT, A
is the midpoint of SR.
2. MA ≅ TA, SA ≅ RA
3. ∠MAS ≅ ∠TAR
4. ∆MAS ≅ ∆TAR
5. ∠M ≅ ∠T
6. MS ║ TR
Reasons:
1. Given
2. Definition of a midpoint
A
M
T
R
S
4. Given: A is the midpoint of MT, A is the
midpoint of SR.
Prove: MS ║TR.
Statements:
1. A is the midpoint of MT, A
is the midpoint of SR.
2. MA ≅ TA, SA ≅ RA
3. ∠MAS ≅ ∠TAR
4. ∆MAS ≅ ∆TAR
5. ∠M ≅ ∠T
6. MS ║ TR
Reasons:
1. Given
2. Definition of a midpoint
3. Vertical Angles Theorem
A
M
T
R
S
5. Given: A is the midpoint of MT, A is the
midpoint of SR.
Prove: MS ║TR.
Statements:
1. A is the midpoint of MT, A
is the midpoint of SR.
2. MA ≅ TA, SA ≅ RA
3. ∠MAS ≅ ∠TAR
4. ∆MAS ≅ ∆TAR
5. ∠M ≅ ∠T
6. MS ║ TR
Reasons:
1. Given
2. Definition of a midpoint
3. Vertical Angles Theorem
4. SAS Congruence
Postulate
A
M
T
R
S
6. Given: A is the midpoint of MT, A is the
midpoint of SR.
Prove: MS ║TR.
Statements:
1. A is the midpoint of MT, A
is the midpoint of SR.
2. MA ≅ TA, SA ≅ RA
3. ∠MAS ≅ ∠TAR
4. ∆MAS ≅ ∆TAR
5. ∠M ≅ ∠T
6. MS ║ TR
Reasons:
1. Given
2. Definition of a midpoint
3. Vertical Angles Theorem
4. SAS Congruence
Postulate
5. Corres. parts of ≅ ∆’s are ≅
A
M
T
R
S
7. Given: A is the midpoint of MT, A is the
midpoint of SR.
Prove: MS ║TR.
Statements:
1. A is the midpoint of MT, A
is the midpoint of SR.
2. MA ≅ TA, SA ≅ RA
3. ∠MAS ≅ ∠TAR
4. ∆MAS ≅ ∆TAR
5. ∠M ≅ ∠T
6. MS ║ TR
Reasons:
1. Given
2. Definition of a midpoint
3. Vertical Angles Theorem
4. SAS Congruence
Postulate
5. Corres. parts of ≅ ∆’s are ≅
6. Alternate Interior Angles
Converse.
A
M
T
R
S
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