In a quadrilateral abcd, the diagonals intersect at point t. byron has used the alternate interior angles theorem to show that angle dac is congruent to angle bca and that angle bac is congruent to dca.
which of the following can byron use prove that side ad is equal to side bc?

a. ac = ac
b. ac = db
c. db = db
d. tb = td

A. AC = AC

Step-by-step explanation:

Given: In a quadrilateral ABCD, the diagonals intersect at point T.

Byron has used the Alternate Interior Angles Theorem to show ∠DAC≅∠BCA

and ∠BAC≅∠DCA

From the given options, we can only use option A i.e. AC=AC [reflexive property] such that

In ΔADC and ΔABC

∠DAC≅∠BCA  [ given ]

∠BAC≅∠DCA  [ given ]

AC=AC [reflexive property]

⇒ΔADC ≅ ΔABC [ASA congruency criteria]

Thus AD=BC [corresponding parts of congruent triangles are congruent]