Given: AD ≅ BC and AD ∥ BC Prove: ABCD is a parallelogram. Statements Reasons 1. AD ≅ BC; AD ∥ BC 1. given 2. ∠CAD and ∠ACB are alternate interior ∠s 2. definition of alternate …

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asked Mar 10, 2018 210k views

2 Answers

Cameron Forward · Answer 1 · 2018-03-11T12:43:51+0000

Given: It is given that
$AD \cong BC$ and
$AD \parallel BC$ .

To Prove: ABCD is a parallelogram.

Statements

1.
$AD \cong BC$ and
$AD \parallel BC$

Reason: Given

2.
$\angle CAD, \angle ACB$ are alternate interior angles

Reason: Def of alternate interior angles

3.
$\angle CAD \cong \angle ACB$

Reason: Alternate interior angles are congruent

4.
$AC \cong AC$

Reason: Reflexive property

5.
$\Delta CAD \cong \Delta ACB$

Reason: SAS congruency theorem

6.
$AB \cong CD$

Reason: Corresponding Parts of Congruent triangles are Congruent (CPCTC)

7. ABCD is a parallelogram

Reason: Parallelogram Side Theorem

Bananaforscale · Answer 2 · 2018-03-14T10:20:51+0000

Given: AD ≅ BC and AD ∥ BC

Prove: ABCD is a parallelogram.

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. Corresponding Parts of Congruent triangles are Congruent (CPCTC)

7. ABCD is a parallelogram 7. parallelogram side theorem