Question

Given: AE =BD: CD=CE Prove: 0= BC 1) 4E = BD; CD=CE 1, Given 2) HE = 40 +CE 2) Segment Addition Postulate 3) BD = 40 +CD 3) Subtraction Property of Equality 4) AC-CD = 17) 4) Symmetric Property of Equality 5) BD = BC-CD 5) Segment Addition Postulate 6) 4C -CD = BC - CD 6) Transitive Property of Equality 7.40 = BC 7 Substitution Property of Equality

Answer 1

AE=BD, CD=CE. Given.

AE=AC+CE Segment Addition postulate.

BD=BC+CD Segment Addition postulate.

Since AE=BD,

AC+CE=BC+CD Transitive property

Since CD=CE , put CE for CD.

AC+CE=BC+CE. Substitution property

Hence,

AC=BC.