Triangles BCA and DKE are rectangular, B = D = 90 degrees, BC = DE, C = E.

Triangles BCA and DKE are rectangular, B = D = 90 degrees, BC = DE, C = E. Prove that the hypotenuses of the triangles BCA and DKE are equal.

Let us prove the equality of triangles ABC and DKE.

Triangles ABC and DKE are rectangular, since angle B = D = 90, leg BC = DE, and acute angle ACB = KED.

Then right-angled triangles ABC and DKE are equal in leg and adjacent acute angle, the second sign of equality of right-angled triangles.

Then the hypotenuse AC = KE, as required.