3. Given: ABCE is a rectangle. D is the midpoint of E.Prove: AD BDStatements1) ABCE is a rectangle. D is the midpoint of CE. 2) _AED __BCD3) AE = BC4)?5)?6)?Reasons1) Given2) Def. of Rectangle3) Def. of Rectangle4) ?5) ?6)?
Accepted Solution
A:
Answer with Step-by-step explanation:We are given that ABCE is a rectangle .Rectangle is that quadrilateral in which opposite sides are equal and each is equal to 90 degrees.D is the midpoint of E.We have to prove that [tex]AD\cong BD[/tex]Statement:1 ABCE is a rectangle.D is the mid point of CEReason: Given Statement 2:[tex]\angle AED\cong \angle BCD[/tex]Reason:By definition of rectangle Statement:3 AE=BCReason: By definition of rectangleStatement 4:[tex]ED=DC[/tex]Reason: By definition of midpoint because D is the midpoint of side ECStatement 5:[tex]\triangle AED\cong \triangle BCD[/tex]Reason:SAS postulateStatement: 6 [tex]AD\cong BD[/tex]Reason:CPCTHence proved.