Question

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)?

Answer 1

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
`AD\cong BD`

Statement:1 ABCE is a rectangle.D is the mid point of CE

Reason: Given

Statement 2:
`\angle AED\cong \angle BCD`

Reason:By definition of rectangle

Statement:3 AE=BC

Reason: By definition of rectangle

Statement 4:
`ED=DC`

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

Statement 5:
`\triangle AED\cong \triangle BCD`

Reason:SAS postulate

Statement: 6
`AD\cong BD`

Reason:CPCT

Hence proved.