Answer:
In the case of an isosceles trapezium, we can use the following pair of congruent triangles to show that the diagonals are congruent:
Triangle ABC: This triangle is formed by the upper base of the trapeze and the two diagonals, i.e., segments AB, AC and BC.
ACD triangle: This triangle is formed by the lower base of the trapeze and the two diagonals, namely the AD, AC and CD segments.
These two triangles are congruent, and we can use the SAA (Side-Angle-Angle) congruence criterion to prove it. The corresponding sides of the ABC and ACD triangles are congruent because they are the same segments of the trapezoid diagonals.
Using the SAA criterion, we can state that the ABC triangle is congruent with the ACD triangle, which means that their corresponding diagonals, AC and CD, are congruent.
Explanation: