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# 4.5 using congruent triangles

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### 4.5 using congruent triangles

1. 1. 4.6 Using Congruent Triangles
2. 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. 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. 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. 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. 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. 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