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2 years ago

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

Mathematics

1 answer:

Georgia [21]2 years ago

7 0

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.

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