Math Question

In the diagram, quadrilateral \( A B C D \) has diagonal \( \overline{B D}, \overline{A B} \cong \overline{D C} \), and \( \overline{A D} \cong \overline{B C} \).
To prove that a quadrilateral with two pairs of opposite congruent sides is a parallelogram, Garrett first wants to prove that \( \triangle A B D \cong \triangle C D B \). Which congruence theorem will Garrett use to prove that \( \triangle A B D \cong \triangle C D B \) ?
Angle-Side-Angle Angle-Angle-Side
Side-Side-Side Side-Angle-Side
After proving that \( \triangle A B D \cong \triangle C D B \), how can Garrett prove that \( A B C D \) is a parallelogram? Complete the statement.
*, \( \angle A B D \cong \angle C D B . \) So,
by the
-. Similarly, since \( \angle A D B \cong \angle C B D \), \( \quad \)-. So, \( A B C D \) is a parallelogram since its opposite sides are parallel.



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