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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

Respuesta :

isyllus

Answer: 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.      

Ver imagen isyllus
amorj234

Answer:

Answer: 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.      

Step-by-step explanation:

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