Question

statements reasons 1 ad ≅ bc, ad || bc 1 given 2 ∠cad and ∠acb are alternate interior ∠s 2 definition of alternate interior angles 3 ∠cad ≅ ∠acb 3 alternate interior angles are congruent 4 ac ≅ ac 4 reflexive property 5 △cad ≅ △acb 5 sas congruency theorem 6 ab ≅ cd 6 ? 7 abcd is a parallelogram 7 parallelogram side theorem what is the missing reason in step 6? ∘ sss congruency theorem ∘ cpctc ∘ definition of a parallelogram ∘ opposite sides in a parallelogram are congruent

Explanation:

Step1: Analyze the previous steps

We have shown that \(\triangle CAD\cong\triangle ACB\) (by SAS congruency theorem in step 5).

Step2: Recall the property of congruent triangles

When two triangles are congruent, their corresponding parts are congruent. This property is called CPCTC (Corresponding Parts of Congruent Triangles are Congruent).

Answer:

CPCTC