In the diagram, AB and DC are parallel lines of equal length - OCR - GCSE Maths - Question 9 - 2020 - Paper 1

To prove that angle DAB is equal to angle BCD, we will use the properties of parallel lines and transversals.

1. Identify Corresponding Angles: Since AB is parallel to DC and AD serves as a transversal, the angles formed at points A and B are corresponding angles.

2. Equal Lengths: Given that AB and DC are of equal length, we can also claim that triangles DAB and BCD are congruent by the Side-Angle-Side (SAS) criterion, being that:

   • AD = BC (equal lengths)
   • AB = DC (given that they are parallel and of equal length)
   • The angle at A (angle DAB) is equal to the angle at B (angle BCD) based on the property of congruence.

3. Conclusion: Therefore, because corresponding angles formed by the transversal are equal in measure, we conclude that angle DAB = angle BCD.