Mathematics
In quadrilateral ACBD, AC = AD and AB bisects ∠A. Show that Δ ABC ≅ Δ ABD. What can you say about BC and BD?
Triangles
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Answer
Given :
AC = AD
AB bisects ∠A i.e, ∠CAB = ∠DAB
In Δ ABC and Δ ABD
⇒ AB = AB (Common side)
⇒ ∠CAB = ∠DAB (Proved above)
⇒ AC = AD (Given)
∴ Δ ABC ≅ Δ ABD (By S.A.S. Congruence rule)
⇒ BC = BD (By C.P.C.T.)
Hence, BC and BD are of equal length.
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