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Question

A diagonal of a parallelogram divides it into :


  1. None of the above
  2. two congruent triangles

  3. two equilateral triangles

  4. two isosceles triangle


Solution

The correct option is B

two congruent triangles


A diagonal of a parallelogram divides it into two congruent triangles.

Proof - In a parallelogram ABCD, ABCD and BCAD.
AC is the transversal for the parallel pair of lines.
In ABC and  ADC :
ACB =  CAD (alternate interior angles)
BAC =   DCA (alternate interior angles)
AC=CA 
  ABC  ADC. ( ASA congruency )
Hence proved.
 

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