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Given: E is the midpoint of DF Prove: 2DE = DF

D E F. Given: E is the midpoint of DF Prove: 2DE = DF. E is the midpoint DF Given DE = EF Definition of midpoint DE + EF = DF Segment addition postulate DE + DE = DF Substitution property 2DE = DF Simplify (like terms) 2DE = DF QED.

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Given: E is the midpoint of DF Prove: 2DE = DF

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  1. D E F • Given: E is the midpoint of DF • Prove: 2DE = DF E is the midpoint DF Given DE = EF Definition of midpoint DE + EF = DF Segment addition postulate DE + DE = DF Substitution property 2DE = DF Simplify (like terms) 2DE = DF QED

  2. A B C • Given: B is the midpoint of AC • Prove: AC = 2AB B is the midpoint AC Given AB = BC Definition of midpoint AB + BC = AC Segment addition postulate AB + AB = AC Substitution property 2AB = AC Simplify (like terms) AC = 2AB Symmetric property AC = 2AB QED

  3. H I J • Given: I is the midpoint of HJ • Prove: HJ = 2IJ I is the midpoint HJ Given HI = IJ Definition of midpoint HI + IJ = HJ Segment addition postulate IJ + IJ = HJ Substitution property 2IJ = HJ Simplify (like terms) HJ = 2IJ Symmetric property HJ = 2IJ QED

  4. X Y Z • Given: Y is the midpoint of XZ • Prove: XZ = 2XY Y is the midpoint XZ Given XY = YZ Definition of midpoint XY + YZ = XZ Segment addition postulate XY + XY = XZ Substitution property 2XY = XZ Simplify (like terms) XZ = 2XY Symmetric property XZ = 2XY QED

  5. P Q R • Given: Q is the midpoint of PR • Prove: PR = 2PQ Q is the midpoint PR Given PQ = QR Definition of midpoint PQ + QR = PR Segment addition postulate PQ + PQ = PR Substitution property 2PQ = PR Simplify (like terms) PR = 2PQ Symmetric property PR = 2PQ QED

  6. T U V • Given: U is the midpoint of TV • Prove: TV = 2TU U is the midpoint TV Given TU = UV Definition of midpoint TU + UV = TV Segment addition postulate TU + TU = TV Substitution property 2TU = TV Simplify (like terms) TV = 2TU Symmetric property TV = 2TU QED

  7. A B C D • Given: B is the midpoint of AC C is the midpoint of BD • Prove: AD = 3AB B is the midpoint of AC; Given C is the midpoint of BD Given AB = BC BC = CD Definition of midpoint AB + BC + CD = AD Segment Addition Postulate AB + BC + BC = AD Substitution Property AB + AB + AB = AD Substitution Property 3AB = AD Simplify (Like Terms) AD = 3AB Symmetric Property AD = 3AB QED

  8. E F G H • Given: F is the midpoint of EG G is the midpoint of FH • Prove: EH = 3EF F is the midpoint of EG; Given G is the midpoint of FH Given EF = FG FG = GH Definition of midpoint EF + FG + GH = EH Segment Addition Postulate EF + FG + FG = EH Substitution Property EF + EF + EF = EH Substitution Property 3EF = EH Simplify (Like Terms) EH = 3EF Symmetric Property EH = 3EF QED

  9. X Y Z W • Given: Y is the midpoint of XZ Z is the midpoint of YW • Prove: XW = 3XY Y is the midpoint of XZ; Given Z is the midpoint of YW Given XY = YZ YZ = ZW Definition of midpoint XY + YZ + ZW = XW Segment Addition Postulate XY + YZ + YZ = XW Substitution Property XY + XY + XY = XW Substitution Property 3XY = XW Simplify (Like Terms) XW = 3XY Symmetric Property XW = 3XY QED

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