Question

In a figure BC is parallel to AE and CD is parallel to BE. Prove that area of triangle ABC is equal to area of triangle EBD​

Answer 1

Step-by-step explanation:

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Answer 2

Area of triangle Δ ABC is equal to area of Δ EBD.

Step-by-step explanation:

See the attached diagram.

Given AE ║ BC and then ED ║ BC.

Again, given that BE ║ CD

Therefore, BCDE is a parallelogram.

Hence, area of Δ BCD = area of Δ EBD {Since diagonals divide the parallelogram into equal triangles}

Now, Δ ABC and Δ BCD has the same area.

{Since they are between same parallel lines AD and BC and their base is the same BC}

Therefore, area of triangle Δ ABC is equal to area of Δ EBD. (Proved)