Free help with homework

Why join Brainly?

  • ask questions about your assignment
  • get answers with explanations
  • find similar questions


Theorem : Parallelograms on the same base and between the same parallels are equal in area.
Given:  Two parallelograms ABCD and EFCD
To prove: ar (ABCD) = ar (EFCD).
Proof : Two parallelograms ABCD and EFCD, on the same base DC and between the same parallels.
In Δ ADE and Δ BCF,
∠ DAE = ∠ CBF (Corresponding angles from AD || BC and transversal AF) (1)
∠ AED = ∠ BFC (Corresponding angles from ED || FC and transversal AF) (2) Therefore, ∠ ADE = ∠ BCF (Angle sum property of a triangle) (3)
Also, AD = BC (Opposite sides of the parallelogram ABCD) (4)
So, Δ ADE ≅ Δ BCF [By ASA rule, using (1), (3), and (4)]
Therefore, ar (ADE) = ar (BCF) (Congruent figures have equal areas) (5)
Now,adding ar (EDCB) both the sides,
 ar (ADE) + ar (EDCB) = ar (BCF)+ ar (EDCB) ar (ABCD) = ar (EFCD)
 So, parallelograms ABCD and EFCD are equal in area.
0 0 0
plzzzzzzz mark as the best..........
The Brain
  • The Brain
  • Helper
Not sure about the answer?
Learn more with Brainly!
Having trouble with your homework?
Get free help!
  • 80% of questions are answered in under 10 minutes
  • Answers come with explanations, so that you can learn
  • Answer quality is ensured by our experts