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? (5 points) Select one: a. AB ≅ DC b. AC ≅ DB c. DA ≅ BC d. TA ≅ TC (PLEASE GIVE FULL ANSWER)

C. DA ≅ BC.

Step-by-step explanation:

Hm... The absence of diagrams makes this hard to picture, but uh... I drew out a parallelogram to visualize this.

If you draw it out, you can see that there are two triangles: triangle ATD and triangle CTB, where angle TAD corresponds to angle TCB, angle ATD corresponds to angle CTB, and angle TDA corresponds to angle TBC.

Since Jasmine wants to prove that the two triangles are congruent, she can use one of the proofs.

Since she already has two angles, she can use either ASA or AAS. That would require either segments BC and DA to be congruent, or segments TA and TC to be congruent.

To be safe, I would say you can use ASA (Angle-Side-Angle) to say that the two triangles are congruent, or that C. DA ≅ BC.

Hope this helps!

the answer for this question is 38

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