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In kite ABCD with AB = AD and CB = CD, why is triangle ABC congruent to triangle ADC?

Class 8Kites and TrapeziumsQuadrilaterals
  • ARHS: both are right triangles
  • BThey are not congruent
  • CSSS: AB = AD, CB = CD and AC is common
  • DASA: two angles and the side between them

Step-by-Step Solution

All three sides match: AB = AD, CB = CD and AC is shared. So the triangles are congruent by SSS, which is why AC bisects ∠A and ∠C.
Answer: C) SSS: AB = AD, CB = CD and AC is common

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