Question

The diagonals of a Quadrilateral divide it into four congruent triangles. The Quadrilateral is a _____________.

• A. Parallelogram
• B. Rectangle
• C. Rhombus
• D. None of the above

Answer 1

The correct option is C Rhombus

If ABCD is a rhombus, then in △AOB△AOB and △COD△COD
AO=COAO=CO, DO=OBDO=OB and ∠AOB=∠COD∠AOB=∠COD
∴△AOB∴△AOB and △COD△COD are congruent.
Again in △AOD△AOD and △AOB△AOB
AD=ABAD=AB, AO is common and DO=OBDO=OB
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∴△AOD∴△AOD and △AOB△AOB are congruent.
bUT △AOB△AOB and △COD△COD are congruent.
Thus all the four triangles are congruent
So, it is possible only when it is rhombus.