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1 year 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:

tiny-mole [99]1 year ago

6 0

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

ira [324]1 year ago

5 0

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

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Assuming the table is rectangular:
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Therefore:
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Using completing the square method:
x^2 + 18x + 81 </span><span>≤ 175 + 81
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|x + 9| </span><span>≤ sqrt(256)
|x + 9| </span><span>≤ +-16
-16 </span>≤ x + 9 <span>≤ 16
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</span>-25 ≤ x <span>≤ 7
</span><span>
But x > 0 (there are no negative measurements):
</span><span>
Therefore, the interval 0 < x </span><span>≤ 7 represents the possible widths.</span><span>

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