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

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02-05-2017
Mathematics

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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

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isyllus isyllus · Answer 1 · 2019-03-04T11:35:04+01:00

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.

amorj234 amorj234 · Answer 2 · 2020-11-11T18:37:08+01:00

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.