Match the following reasons with the statements given. complete the proof for the theorem 4-18 mentioned above. 1. do = ob, ao = oc if two sides = and ||, then a parallelogram. 2. doc = aob vertical angles are equal. 3. triangle cod congruent to triangle aob cpcte 4. 1 = 2, ab = dc given 5. ab||dc if alternate interior angles =, then lines parallel. 6. abcd is a parallelogram sas

Please see attachment.

Solution:

We need to match the column using column proof. Please see the attachment for matching column.

In ΔDOC and ΔBOA

      DO=BO               (Given)

 ∠DOC=∠BOA          (Vertically Opposite angle)

      OC=OA               (Given)

∴   ΔDOC ≅ ΔBOA   by  SAS congruence property

     ∠1=∠2  and  AB=DC     By CPCTE

Thus, AB||DC   (∠1 and ∠2 are alternate angles equal then lines parallel)

ABCD is a parallelogram. ( If two sides equal and parallel then a parallelogram.

Below is matched table.

DO = OB, AO = OC ⇒ Given      

∠ DOC =∠ AOB      ⇒ Vertical angles are equal

∆COD ≅ ∆AOB⇒  SAS             CPCTE

∠1 = ∠2,  AB = DC⇒  CPCTE          

AB||DC                 ⇒  If alternate interior angles =, then lines parallel

ABCD is a parallelogram ⇒ If two sides = and ||, then a parallelogram

Please see attachment for figure and matching.      

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