Respuesta :
The option that Thomas can use to prove that triangle ATD is congruent to triangle CTB is C. DA ≅ BC.
How to illustrate the information
This question is based on the concept of congruent. In quadrilateral ABCD, the diagonals intersect at point T. By the alternate interior angles theorem :
Angle DAC is congruent to angle BCA and angle ADB is congruent to angle CBD.
The alternate interior angles theorem states that, when two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent.
In the given quadrilateral ABCD,
DAC ≅ BCA
ADB ≅ CBD
And to prove that ATD ≅ CTB, then, DA ≅ BC.
Therefore, the correct option is C.
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Complete question:
In quadrilateral ABCD, the diagonals intersect at point T. Thoma has used the Alternate Interior Angles Theorem to show that angle DAC is congruent to angle BCA and that angle ADB is congruent to angle CBD.
Which of the following can Thoma use to prove that triangle ATD is congruent to triangle CTB?
AB ≅ DC
AC ≅ DB
DA ≅ BC
AC ≅ AC
