This document proves that the area of parallelogram ABCD is equal to the area of parallelogram EFCD. It shows that triangle ADE is congruent to triangle BCF based on their corresponding angles and opposite sides of the parallelograms. Since congruent triangles have equal areas, and the areas of the parallelograms can be expressed as the sum of the two triangles' areas, the areas of the two parallelograms must be equal.

3. AREA
OF
PARALLELOGRAM
ABCD = AREA OF
PARALLELOGRAM
EFCD

4.  IN
∆ADE AND ∆BCF,
 ANGLE DAE = CBF (CORRESPONDING
ANGLES FROM AD||BC AND
TRANSVERSAL AF)(1)
 ANGLE AED = BFC (CORRESPONDING
ANGLES FROM ED||FC AND
TRANSVERSAL AF)(2)
 THEREFORE,ANGLE ADE = BCF(ANGLE
SUM PROPERTY OF A TRIANGLE)(3)

5. ALSO, AD=BC(OPPOSITE SIDES OF PARALLELOGRAM
ABCD)(4)
 SO, ∆ADE IS CONGRUENT TO ∆BCF(BY ASA
RULE,USING(1),(3),(4))
 THEREFORE,ar(ADE) = area(BCF)(CONGRUENT FIGURE
HAVE EQUAL AREA)
 NOW, ar(ABCD) = area(ADE) + area(EDCB)
= area(BCF) + area(EDCB)
= area(EFCD)
 SO, PARALLELOGRAMS ABCD AND EFCD ARE EQUAL
IN AREA.
(HENCE PROVED)


6. THANK YOU
BY-SITIKANTHA MISHRA
R NO -36
IX A