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Two isosceles triangles share the same base BC on opposite sides, with apexes A and D, where AB = AC and DB = DC.
Which statement is always true about line AD?

Class 9Properties of Isosceles TrianglesGeometry — Triangles
  • AAD is the perpendicular bisector of BC
  • BAD is parallel to BC
  • CAD equals BC
  • DAD bisects neither BC nor any angle

Step-by-Step Solution

Both A and D are equidistant from B and C, so both lie on the perpendicular bisector of BC; hence line AD is that perpendicular bisector.
Answer: A) AD is the perpendicular bisector of BC

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