Question

In Fig. 10.22, the sides BA and CA have been produced such that: BA = AD and CA = AE.

Answer 1

In the given figure the sides BA and CA have been produced such that BA=AD and CA=AE.

Prove that the segment DE||BC

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

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