Question

in quadrilateral badc, ab = ad and bc = dc. the line ac is a line of symmetry for this quadrilateral. a. based on the line of symmetry, explain why the diagonals ac and bd are perpendicular. type your response in the space below.

Explanation:

Step1: Recall line - of - symmetry property

A line of symmetry divides a figure into two congruent parts. For a quadrilateral with line of symmetry AC, points B and D are mirror - images of each other across AC.

Step2: Consider intersection of diagonals

Let the intersection of AC and BD be point O. Since B and D are mirror - images across AC, the line segment BD is perpendicular to the line of symmetry AC at the point of intersection O. So, the diagonals AC and BD are perpendicular.

Answer:

The diagonals AC and BD are perpendicular because the line of symmetry AC divides the quadrilateral into two congruent parts where B and D are mirror - images of each other across AC. At the intersection of AC and BD, the line segment BD must be perpendicular to the line of symmetry AC.