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4.5 using congruent triangles

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    4.5 using congruent triangles 4.5 using congruent triangles Presentation Transcript

    • 4.6 Using Congruent Triangles
    • Given: A is the midpoint of MT, A is the midpoint of SR. Prove: MS ║TR.
      • Statements:
      • A is the midpoint of MT, A is the midpoint of SR.
      • MA ≅ TA, SA ≅ RA
      •  MAS ≅  TAR
      • ∆ MAS ≅ ∆TAR
      •  M ≅  T
      • MS ║ TR
      • Reasons:
      • Given
    • Given: A is the midpoint of MT, A is the midpoint of SR. Prove: MS ║TR.
      • Statements:
      • A is the midpoint of MT, A is the midpoint of SR.
      • MA ≅ TA, SA ≅ RA
      •  MAS ≅  TAR
      • ∆ MAS ≅ ∆TAR
      •  M ≅  T
      • MS ║ TR
      • Reasons:
      • Given
      • Definition of a midpoint
    • Given: A is the midpoint of MT, A is the midpoint of SR. Prove: MS ║TR.
      • Statements:
      • A is the midpoint of MT, A is the midpoint of SR.
      • MA ≅ TA, SA ≅ RA
      •  MAS ≅  TAR
      • ∆ MAS ≅ ∆TAR
      •  M ≅  T
      • MS ║ TR
      • Reasons:
      • Given
      • Definition of a midpoint
      • Vertical Angles Theorem
    • Given: A is the midpoint of MT, A is the midpoint of SR. Prove: MS ║TR.
      • Statements:
      • A is the midpoint of MT, A is the midpoint of SR.
      • MA ≅ TA, SA ≅ RA
      •  MAS ≅  TAR
      • ∆ MAS ≅ ∆TAR
      •  M ≅  T
      • MS ║ TR
      • Reasons:
      • Given
      • Definition of a midpoint
      • Vertical Angles Theorem
      • SAS Congruence Postulate
    • Given: A is the midpoint of MT, A is the midpoint of SR. Prove: MS ║TR.
      • Statements:
      • A is the midpoint of MT, A is the midpoint of SR.
      • MA ≅ TA, SA ≅ RA
      •  MAS ≅  TAR
      • ∆ MAS ≅ ∆TAR
      •  M ≅  T
      • MS ║ TR
      • Reasons:
      • Given
      • Definition of a midpoint
      • Vertical Angles Theorem
      • SAS Congruence Postulate
      • Corres. parts of ≅ ∆’s are ≅
    • Given: A is the midpoint of MT, A is the midpoint of SR. Prove: MS ║TR.
      • Statements:
      • A is the midpoint of MT, A is the midpoint of SR.
      • MA ≅ TA, SA ≅ RA
      •  MAS ≅  TAR
      • ∆ MAS ≅ ∆TAR
      •  M ≅  T
      • MS ║ TR
      • Reasons:
      • Given
      • Definition of a midpoint
      • Vertical Angles Theorem
      • SAS Congruence Postulate
      • Corres. parts of ≅ ∆’s are ≅
      • Alternate Interior Angles Converse.