In a quadrilateral abcd, the diagonals intersect at point t. jasmine has used the alternate interior angles theorem to show that angle dac is congruent to angle bca and that angle adb is congruent to cbd.

which of the following can jasmine use prove that triangle atd is congruent to triangle ctb?

ab congruent to dc
ac congruent to db
da congruent to bc
ta congruent to tc

The correct answer is:

ta is congruent to tc.

explanation:

we already know that  ∠cbd is congruent to  ∠adb and  ∠dac is congruent to  ∠bca.  we need to have a side congruent from each one in order to prove congruence.   

since the sides intersect at the same angles, this means ad must be congruent to bc.  this gives us two angles and a non-included side, which is the aas congruence theorem.

The correct answer for the question that is being presented above is this one: "da congruent to bc."  in a quadrilateral abcd, the diagonals intersect at point t. jasmine has used the alternate interior angles theorem to show that angle dac is congruent to  angle bca and that angle adb is congruent to cbd.