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In a kite ABCD, AB = AD and CB = CD. The diagonal AC is drawn.
Which rule proves triangle ABC congruent to triangle ADC, and what does it show about diagonal AC?

Class 9SSS and RHS CongruenceGeometry — Triangles
  • ASSS; AC bisects angles A and C
  • BRHS; AC is the hypotenuse
  • CAAA; AC is the longest side
  • DSSA; AC is bisected

Step-by-Step Solution

AB=AD, CB=CD, AC=AC (common): SSS gives triangle ABC ≅ triangle ADC. By CPCT, angle BAC = angle DAC and angle BCA = angle DCA, so AC bisects angles A and C.
Answer: A) SSS; AC bisects angles A and C

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