Question

ABCD is a rectangle BD is the diagonal of the rectangle. Write the entire congruence criterion which can be
used to show triangle ABD congruent to triangle DCB.​

Answer 1

Here is what is given: Rectangle ABCD

Here is what you need to prove: segment AC ≅ segment BD

Since ABCD is a rectangle, it is also a parallelogram.

Since ABCD is a parallelogram, segment AB ≅ segment DC because opposite sides of a parallelogram are congruent.

BC ≅ BC by the Reflexive Property of Congruence.

Furthermore, ∠ABC and ∠DCB are right angles by the definition of rectangle.

∠ABC ≅ ∠DCB since all right angles are congruent.

Summary

segment AB ≅ segment DC

∠ABC ≅ ∠DCB

BC ≅ BC

Therefore, by SAS, triangle ABC ≅ triangle DCB.

Since triangle ABC ≅ triangle DCB, segment AC ≅ segment BD