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2 months ago

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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?

2 answers:

Svet_ta [12.7K]2 months ago

6 0

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

To Prove: ABCD is a parallelogram.

Statements

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

Reason: Provided

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

Reason: Definition of alternate interior angles

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

Reason: Congruence of alternate interior angles

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: Theorem regarding sides of parallelograms

tester [12.3K]2 months ago

5 0

Given: AD ≅ BC and AD ∥ BC

Prove: ABCD is a parallelogram.

Statements Reasons

1. AD ≅ BC; AD ∥ BC 1. provided

2. ∠CAD and ∠ACB are alternate interior angles 2. definition of alternate interior angles

3. ∠CAD ≅ ∠ACB 3. congruence of alternate interior angles

4. AC ≅ AC 4. reflexive property

5. △CAD ≅ △ACB 5. SAS congruency theorem

6. AB ≅ CD 6. Congruent triangles have congruent corresponding parts (CPCTC)

7. ABCD is a parallelogram 7. theorem for sides of parallelograms

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