Question

prove that the parallelogram on the same base and between the same parallel lines are equal in area ?

Answer 1

Answer:

Theorem: Parallelograms on the same base and between the same parallels are equal in area.

Proof: Consider the figure presented above. Can you see that

Δ

B

C

E

and

Δ

A

D

F

will be congruent? This is easy to show. We have:

BC = AD (opposite sides of a parallelogram are equal)

∠

B

C

E

=

∠

A

D

F

(corresponding angles)

∠

B

E

C

=

∠

A

F

D

(corresponding angles)

By the ASA criterion, the two triangles are congruent, which means that their areas are equal. Now,

area(ABCD) = area(ABED) + area(

Δ

B

C

E

)

Similarly,

area(ABEF) = area(ABED) + area(

Δ

A

D

F

)

Clearly,

area(ABCD) = area(ABEF)

Answer 2

Step-by-step explanation:

by Simple and easy step plz visit this picture