Question

in quadrilateral badc, ab = ad and bc = dcs. the line ac is a line of symmetry for this quadrilateral.

1. based on the line of symmetry, explain why angles abc and adc have the same measure.

Explanation:

Since line \(AC\) is a line of symmetry, when we reflect the quadrilateral \(BADC\) over line \(AC\), point \(B\) maps to point \(D\) (because \(AB = AD\)) and point \(C\) maps to itself. The angle \(\angle ABC\) is mapped to \(\angle ADC\) under this reflection. A reflection is a rigid transformation that preserves angle - measure.

Answer:

Angles \(ABC\) and \(ADC\) have the same measure because a reflection over the line of symmetry \(AC\) maps \(\angle ABC\) to \(\angle ADC\), and reflections (as rigid transformations) preserve the measure of angles.