4.6 Using Congruent Triangles

Given: A is the midpoint of MT, A is themidpoint of SR.Prove: MS ║TR.

Statements:1. A is the midpoint of MT,

A is the midpoint of SR.2. MA ≅ TA, SA ≅ RA3. MAS ≅ TAR4. ∆MAS ≅ ∆TAR5. M ≅ T6. MS ║ TR

Reasons:1. Given

A

M

T

R

S

Given: A is the midpoint of MT, A is themidpoint of SR.Prove: MS ║TR.

Statements:1. A is the midpoint of MT,

A is the midpoint of SR.2. MA ≅ TA, SA ≅ RA3. MAS ≅ TAR4. ∆MAS ≅ ∆TAR5. M ≅ T6. MS ║ TR

Reasons:1. Given

2. Definition of a midpoint

A

M

T

R

S

Given: A is the midpoint of MT, A is themidpoint of SR.Prove: MS ║TR.

Statements:1. A is the midpoint of MT,

A is the midpoint of SR.2. MA ≅ TA, SA ≅ RA3. MAS ≅ TAR4. ∆MAS ≅ ∆TAR5. M ≅ T6. MS ║ TR

Reasons:1. Given

2. Definition of a midpoint3. Vertical Angles

Theorem

A

M

T

R

S

Given: A is the midpoint of MT, A is themidpoint of SR.Prove: MS ║TR.

Statements:1. A is the midpoint of MT,

A is the midpoint of SR.2. MA ≅ TA, SA ≅ RA3. MAS ≅ TAR4. ∆MAS ≅ ∆TAR5. M ≅ T6. MS ║ TR

Reasons:1. Given

2. Definition of a midpoint3. Vertical Angles

Theorem4. SAS Congruence

Postulate

A

M

T

R

S

Given: A is the midpoint of MT, A is themidpoint of SR.Prove: MS ║TR.

Statements:1. A is the midpoint of MT,

A is the midpoint of SR.2. MA ≅ TA, SA ≅ RA3. MAS ≅ TAR4. ∆MAS ≅ ∆TAR5. M ≅ T6. MS ║ TR

Reasons:1. Given

2. Definition of a midpoint3. Vertical Angles

Theorem4. SAS Congruence

Postulate5. Corres. parts of ≅ ∆’s

are ≅

A

M

T

R

S

Given: A is the midpoint of MT, A is themidpoint of SR.Prove: MS ║TR.

Statements:1. A is the midpoint of MT,

A is the midpoint of SR.2. MA ≅ TA, SA ≅ RA3. MAS ≅ TAR4. ∆MAS ≅ ∆TAR5. M ≅ T6. MS ║ TR

Reasons:1. Given

2. Definition of a midpoint3. Vertical Angles Theorem4. SAS Congruence

Postulate5. Corres. parts of ≅ ∆’s

are ≅6. Alternate Interior Angles

Converse.

A

M

T

R

S