What is the missing reason in step 3?

answer choices :
1) triangle angle sum theorem
2) sas congruency theorem
3) sss congruency theorem
4) cpctc

Option 3 is correct

SSS congruency  theorem

Step-by-step explanation:

In ΔADC and ΔCBA

     [Side]                  [Given]

     [Side]                   [Given]

Reflexive property states that any value is equal to itself

     [Side]         [Reflexive Property]

SSS -Side-Side-Side postulates states that  that if three sides of one triangle are congruent to three sides of another triangle, then these two triangles are congruent.

Therefore,

ΔADC ΔCBA            [By SSS]

By CPCT (Corresponding Part of Congruent Triangle]

and

Alternate interior angle states that a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal.

therefore, by definition of  alternate interior angle ;

and are alternate interior angle

also, and are  alternate interior angle

By converse of the alternate interior angle theorem states that  if two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel.

therefore, we have

;

Then,by the definition of parallelogram that a four sided flat shape with straight sides where opposite sides are parallel.

⇒ABCD is parallelogram               hence proved!

step-by-step explanation:

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