To prove that ∆ ABC ≈ ∆ CDA, line AC is an angle bisector of <BCD.
What are congruent triangles?
Two triangles are said to be congruent when they have equal side length and angles when measured.
Given that;
Line AB is perpendicular to line BC
Line AD is perpendicular to line DC.
Line BC is perpendicular to line AD
Therefore the diagonal line is a bisector of both angles <C and A into two equal angles.
This makes ∆ ABC ≈ ∆ CDA