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Question

During the construction of a triangle given its base, a base angle and the sum of other two sides, which of the triangles formed are congruent?


  1. ABC and   AMC
  2.  ABC and  ADC
  3.  ABC and  AMD
  4.  AMC and  AMD


Solution

The correct option is D  AMC and  AMD

Given,
Construction of a triangle given its base, a base angle and sum of other two sides.

If we take AMC and AMD,
DM = MC (perpendicular bisector bisects the line DC)
AMC =  AMD = 90   (perpendicular bisector)
AM = AM (common side)

AMC   AMD  (By SAS Congruency)

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