Question

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. ? 7. ABCD is a parallelogram 7. parallelogram side theorem What is the missing reason in step 6?

Answer 1

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

Answer 2

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