Question

The figure shows an isosceles trapezium with AB=DC.
(a) Show that angle ABC=angle DCB.
(b) Hence show that the diagonals of the trapezium (AC and BD) are equal in length.

A coordinate system is introduced to the trapezium with A(a,b), B(0,0) and D(c,b).

(c) Express the coordinates of C in terms of a and c.
(d) Hence show that the diagonals of the trapezium are equal in length.

Answer 1

can u prove triangle ABC and DBC congruent ??
this will solve both (a) and (b) parts.

Answer 2

those 2 angles are congruent because the lines are parallel.