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In quadrilateral BADC, AB=AD and BC=DC. The line AC is a line of symmetry for this quadrilateral.

Quadrilateral B A D C.

a. Based on the line of symmetry, explain why the diagonals AC and BD are perpendicular.

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Answer:

  a line of symmetry is always the perpendicular bisector of a point and its symmetrical image

Step-by-step explanation:

A line of symmetry is a perpendicular bisector of any segment joining a point and its symmetrical image. B and D are symmetrically located about line AC, so AC must be a perpendicular bisector of BD.

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