Question

In the figure above, BD is the altitude drawn to AC. Triangles ABD and CBD are congruent if _________
A. `AB=BC`
B. AD=CD
C. Either (a) or (b)
D. None of these

Answer 1

Correct Answer - C

`bar(BD)botbar(AC) ACimplies angleBDC=angleBDA=90^(@)`
BD is the common side of `DeltaABD and DeltaCBD`.
(i) If AB=BC ,
`DeltaABD ~=DeltaCBD` ( by RHS ).
(ii) If AD=CD,
`DeltaABD~=DeltaCBD ` (by SAS).
Hence, the correct option is ( c).