Final answer:
To complete the proof by showing the congruence of triangles involving the diagonals of the isosceles trapezoid, we can use SAS (Side-Angle-Side) congruence.
Step-by-step explanation:
To complete the proof by showing the congruence of triangles involving the diagonals of the isosceles trapezoid, we can use SAS (Side-Angle-Side) congruence. Let's consider the isosceles trapezoid ABCD with AB//CD and AB = CD. The diagonals AC and BD intersect at point E. Now, let's prove the congruence of triangles ADE and BCE.
We know that AD = BC (as both are the bases of the isosceles trapezoid), AE = BE (as diagonals of the trapezoid bisect each other), and ∠DAE = ∠CBE (as corresponding angles formed by parallel lines), which gives us the required congruence condition of SAS. Therefore, triangles ADE and BCE are congruent.
Similarly, we can prove the congruence of triangles CDE and ABE using SAS congruence. Hence, we have shown the congruence of triangles involving the diagonals of the isosceles trapezoid using SAS congruence.