Question

prove:
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$$\begin{align*} ab &\\cong cd \\\\ bc &\\cong ad \\end{align*}$$

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$$\begin{figure} \\centering \\includegraphicsscale=0.5{parallelogram_proof.png} \\end{figure}$$

proof:

statements	reasons
2. ?	?
3. draw (overline{ac}), a transversal that cuts two pairs of parallel segments. (overline{ab} \parallel overline{cd}) (overline{bc} \parallel overline{ad})	drawing a line segment
4. (angle cab \cong angle acd) (angle bca \cong angle cad)	alternate interior angles theorem
5. (mangle cab = mangle acd) (mangle bca = mangle cad)	definition of congruent
6. (ac = ac)	reflexive property of equality
7. ?	asa criterion for congruence
8. (overline{ab} \cong overline{cd}) (overline{bc} \cong overline{ad})	corresponding sides of congruent triangles are congruent

1. what are the missing statement and reason in step 2 of the proof?

a. statement: (angle bac \cong angle acd)
reason: alternate interior angles theorem

b. statement: (overline{ab} \parallel overline{cd}), (overline{bc} \parallel overline{ad})
reason: definition of a parallelogram

c. statement: (overline{ab} \cong overline{cd}), (overline{bc} \cong overline{ad})
reason: given

d. statement: (\triangle abc \cong \triangle cda)
reason: sss criterion for congruence

Explanation:

To fill step 2 of the proof for the paralleram, we use the definition of a parallelogram, which states that opposite sides are parallel. This sets up the necessary context for using the alternate interior angles theorem in subsequent steps, and it is a direct consequence of the given information that ABCD is a parallelogram.

Answer:

B. Statement: $\overline{AB} \parallel \overline{CD}$, $\overline{BC} \parallel \overline{AD}$
Reason: definition of a parallelogram