Question

In the the adjoining figure the sides BA and CA have been produced such that BA equal to AD and CA equal to AE prove that DE parallel to BC hint use the concept of alternate angles ​

Answer 1

Answer:

Hi there !!

In ΔADE and ΔABC

BA = AD [ Given ]

CA=AE [ Given ]

∠1 = ∠ 2 [ Vertically opposite angles ]

ΔADE ≅ ΔABC [ SAS ]

SO ,

∠ADE = ∠ABC [ cpct ]

∠ADE and ∠ABC are the alternate interior angles for the line segment DE and BC !!!

Hence ,

DE || BC