Question

In the given figure, ABCD, DCFE and ABFE are parallelogram. Show that ar(ΔADE) = ar(ΔBCF).​

Answer 1

$\huge\bold{\underline{Question:}}$

In the given figure, ABCD, DCFE and ABFE are parallelogram. Show that ar(ΔADE) = ar(ΔBCF)

$\huge\bold{\underline{Answer:}}$

$\red\bigstar$ Given:

In the given figure, ABCD, DCFE and ABFE are parallelogram

$\blue\bigstar$ To find:

Show that ar(ΔADE) = ar(ΔBCF)

$\green\bigstar$ Solution:

☃️ Since ABCD a parallelogram, therefore sides AD and BC are equal.

☃️ Since, DCFE is also a parallelogram, therefore sides DE and FC are equal

☃️ Since, ABFE is also a parallelogram, therefore sides AE and BF are equal.

So, ∆ ADE and ∆ BCF are congruent by S-S-S congruency rule.

.°. Corresponding angles are equal in both triangles

Hence, the areas will be equal.

Therefore, ar(ΔADE) = ar(ΔBCF)

_________________________

Answer 2

★ Given:

In the given figure, ABCD, DCFE and ABFE are parallelogram

★ To find:

Show that ar(ΔADE) = ar(ΔBCF)

★ Solution:

Since ABCD a parallelogram, therefore sides AD and BC are equal.

Since, DCFE is also a parallelogram, therefore sides DE and FC are equal

Since, ABFE is also a parallelogram, therefore sides AE and BF are equal.

So, ∆ ADE and ∆ BCF are congruent by S-S-S congruency rule.

.°. Corresponding angles are equal in both triangles

Hence, the areas will be equal.

Therefore, ar(ΔADE) = ar(ΔBCF)