Question

In quadrilateral ABCD, the diagonals intersect at point T. Thomas has used the Alternate Interior Angles Theorem to show that angle ADB is congruent to angle DBC and that angle DBA is congruent to angle BDC.

HELP ASAP Which of the following can Thomas use to prove that side AB is equal to side DC?

AC ≅ AC
AC ≅ DB
TA ≅ TC
DB ≅ DB

Answer 1

Thomas can prove that AB is equal to DC by showing triangles ATB and CTD are congruent, utilizing the fact that TA is congruent to TC in combination with the alternate interior angles theorem.

Step-by-step explanation:

To prove that side AB is equal to side DC in quadrilateral ABCD where the diagonals intersect at point T, and knowing that angle ADB is congruent to angle DBC and that angle DBA is congruent to angle BDC, Thomas should use the fact that TA ≡ TC. This piece of information suggests that triangles ATB and CTD are congruent by SAS (Side-Angle-Side), as they have a side, an angle, and another side congruent between them—the side being the diagonals' segment AT and CT, and the angles being the congruent angles at the point D. By proving these triangles are congruent, he can establish that AB is congruent to DC, as they would be corresponding sides of these congruent triangles.