Question

In figure 9, if AC = BC, DCA = ECB and CBC = ZAC then Prove that BD = AE. D. E B 1

Answer 1

Step-by-step explanation:

⇒ AC=BC [ C is mid-point of AB ]

⇒ ∠DCA=∠ECB [ Given ]

⇒ ∠DBC=∠EAC [ Given ]

Adding ∠ECD to both sides,

⇒ ∠DCA+∠ECD=∠ECB+∠ECD

⇒ ∠ECA=∠DCB ----- ( 1 )

In △DBC and △EAC

⇒ ∠DCB=∠ECA [ From ( 1 ) ]

⇒ AC=BC [ Given ]

⇒ ∠DBC=∠EAC [ Given ]

∴ △DBC≅△EAC [ By ASA congruence test ]

⇒ DC=EC [ By C.P.C.T ]