Question

ABC,DBC are two triangles in which AC and BD meet at X. AX = DX and BX = CX. Prove that angle A = angle D​

Answer 1

Given :- ABC,DBC are two triangles in which AC and BD meet at X. AX = DX and BX = CX. Prove that angle A = angle D ?

Solution :-

in ∆AXB and ∆DXC we have,

→ AX = DX (given)

→ ∠AXB = ∠DXC (vertically opposite angles.)

→ BX = CX (given.)

So,

→ ∆AXB ≅ ∆DXC . (By SAS congruence. )

therefore,

→ ∠XAB = ∠XDC (By CPCT.)

Hence,

→ ∠A = ∠D . (Proved).

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Answer 2

refer the attachment ↑

angle A= angle D