3. Given: ABCE is a rectangle. D is the midpoint of E.

Prove: AD BD

Statements

1) ABCE is a rectangle. D is the midpoint of CE.

2) _AED __BCD

3) AE = BC

4)?

5)?

6)?

Reasons

1) Given

2) Def. of Rectangle

3) Def. of Rectangle

4) ?

5) ?

6)?

Question

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lublana lublana · Answer 1 · 2019-11-21T10:20:36+01:00

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 CE

Reason: Given

Statement 2:[tex]\angle AED\cong \angle BCD[/tex]

Reason:By definition of rectangle

Statement:3 AE=BC

Reason: By definition of rectangle

Statement 4:[tex]ED=DC[/tex]

Reason: By definition of midpoint because D is the midpoint of side EC

Statement 5:[tex]\triangle AED\cong \triangle BCD[/tex]

Reason:SAS postulate

Statement: 6 [tex]AD\cong BD[/tex]

Reason:CPCT

Hence proved.