Question

Show that parallelograms on the same base between 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

ΔBCE

and

Δ

A

D

F

ΔADF

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

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

∠

B

C

E

∠ B C E

=

∠

A

D

F

∠ A D F

(corresponding angles)

∠

B

E

C

∠ B E C

=

∠

A

F

D

∠ 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

ΔBCE

)

Similarly,

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

Δ

A

D

F

ΔADF

)

Clearly,

area(ABCD) = area(ABEF)

This completes the proof.

$\huge \pink {itzmissirritaing}$