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The bisector of angle A in parallelogram ABCD meets DC at point E.
It is found that DE = AD.
Which pair of equal angles makes triangle ADE isosceles here?

Class 9Conditions for a ParallelogramGeometry — Quadrilaterals
  • Aangle DAE = angle DEA
  • Bangle ADE = angle AED
  • Cangle DAE = angle ADE
  • Dangle AED = angle EAB

Step-by-Step Solution

AE bisects angle A so angle DAE = angle EAB. Since AB is parallel to DC, angle EAB = angle DEA (alternate angles). Hence angle DAE = angle DEA, making triangle ADE isosceles with DE = AD.
Answer: A) angle DAE = angle DEA

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