Question

The figure below shows rectangle ABCD:

The following two-column proof with missing statement proves that the diagonals of the rectangle bisect each other:

Which statement can be used to fill in the blank space?
(A) ∠ABD ≅ ∠DBC
(B) ∠CAD ≅ ∠ACB
(C) ∠BDA ≅ ∠BDC
(D) ∠CAB ≅ ∠ACB

Answer 1

B would be the answer because if you were to search up a picture of alternate interior angles, it would be the same as <CAD and <ACB

Answer 2

(B) ∠CAD≅∠ACB

Explanation:

Given in the question quadrilateral ABCD is a rectangle and a table of two-column proof with missing statement for proves that the diagonals of the rectangle bisect each other.

If we want to prove that the diagonals bisects to each other, then for this first we will prove that ΔADE≅ΔCBE. But given in the two-column proof

∠ADB≅∠CBE , side BC= side AD . ∠CAD ≅ACD must be necessary for to prove that ΔADE≅ΔCBE (ASA postulate). Hence statement ∠CAD ≅ACD can be used to fill in the blank space.