Question

In 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 angle CBD.

Which of the following can Jasmine use to prove that triangle ATD is congruent to triangle CTB?

AB ≅ DC
AC ≅ DB
DA ≅ BC
AC ≅ AC

Answer 1

Answer:

DA equals BC

Step-by-step explanation:

they're parallel

Answer 2

This question is based on the concept of congruent. Therefore, the correct option is C, i.e. DA ≅ BC.

Given:

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

Definition of  alternate interior angles theorem:

The Alternate Interior Angles Theorem states that, when two parallel lines are cut by a transversal , then  resulting alternate interior angles are congruent .

In given quadrilateral ABCD,

$\angle$ DAC ≅ $\angle$ BCA

$\angle$ ADB ≅ $\angle$ CBD

And to prove that $\Delta$ ATD ≅ $\Delta$CTB,

Then,

DA ≅ BC

Therefore, the correct option is C, i.e. DA ≅ BC.

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https://brainly.com/question/25063301