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?

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metchelle metchelle · Answer 1 · 2017-05-22T04:30:18+02:00

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

pinquancaro pinquancaro · Answer 2 · 2018-10-16T07:08:12+02:00

Given: It is given that [tex]AD \cong BC[/tex] and [tex]AD \parallel BC[/tex].

To Prove: ABCD is a parallelogram.

Statements

1. [tex]AD \cong BC[/tex] and [tex]AD \parallel BC[/tex]

Reason: Given

2. [tex]\angle CAD, \angle ACB[/tex] are alternate interior angles

Reason: Def of alternate interior angles

3. [tex]\angle CAD \cong \angle ACB[/tex]

Reason: Alternate interior angles are congruent

4. [tex]AC \cong AC[/tex]

Reason: Reflexive property

5. [tex]\Delta CAD \cong \Delta ACB[/tex]

Reason: SAS congruency theorem

6. [tex]AB \cong CD[/tex]

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

7. ABCD is a parallelogram

Reason: Parallelogram Side Theorem