In a quadrilateral ABCD, the diagonals intersect at point T. Heather has used the Alternate Interior Angles Theorem to show that angle ABD is congruent to angle CDB and that angle BAC is congruent to DCA.

Which of the following can Heather use prove that segment DT is equal to segment TB?

A. AB ≅ DC
B. AC ≅ DB
C. DA ≅ BC
D. AC ≅ AC

Question

In a quadrilateral ABCD, the diagonals intersect at point T. Heather has used the Alternate Interior Angles Theorem to show that angle ABD is congruent to angle CDB and that angle BAC is congruent to DCA.

Which of the following can Heather use prove that segment DT is equal to segment TB?

A. AB ≅ DC
B. AC ≅ DB
C. DA ≅ BC
D. AC ≅ AC

carmelle · Answer

are you sure? i was thinking it was A tbh

carmelle · Answer

ok

carmelle · Answer

B was wrong

Vocaloid · Answer

Late response, but I agree with your original reasoning. Heather is setting up proof that ABCD is a quadrilateral by proving that AB and DC are opposite parallel sides. That way, by proving that the shape is a quadrilateral, she can prove that the diagonals bisect each other and thus DT and TB are equal. In order to do this, AB must be congruent to DC (choice A).