Question

4.
given: abcd is a parallelogram
prove: $ab \cong cd$ and $bc \cong da$

statements | reasons
--- | ---
abcd is a parallelogram | given
| def of parallelogram
$\angle 1 \cong \angle 4$ and $\angle 3 \cong \angle 2$ |
$ac \cong ac$ | reflexive property
$\triangle abc \cong \triangle cda$ |
|
|

Explanation:

Step1: State parallel sides property

$AB \parallel CD$ and $BC \parallel DA$

Step2: Justify alternate interior angles

Alternate Interior Angles Theorem

Step3: Prove triangle congruence

ASA Congruence Postulate

Step4: State corresponding sides congruence

$AB \cong CD$ and $BC \cong DA$

Step5: Justify final congruence

CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

Answer:

Filled two-column proof:

Statements	Reasons
$AB \parallel CD$ and $BC \parallel DA$	Def of parallelogram
$\angle 1 \cong \angle 4$ and $\angle 3 \cong \angle 2$	Alternate Interior Angles Theorem
$AC \cong AC$	Reflexive Property
$\triangle ABC \cong \triangle CDA$	ASA Congruence Postulate
$AB \cong CD$ and $BC \cong DA$	CPCTC (Corresponding Parts of Congruent Triangles are Congruent)