Name: ________________________________________________________ Date: _____________ Ms. Ayinde Geometry CC Entrance Ticket

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Regents Exam Questions G.CO.C.11: Parallelograms 2 Name: ________________________ www.jmap.org

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G.CO.C.11: Parallelograms 2

1 In the diagram below, parallelogram ABCD has diagonals AC and BD that intersect at point E.

Which expression is not always true?1) ∠DAE ≅ ∠BCE2) ∠DEC ≅ ∠BEA3) AC ≅ DB4) DE ≅ EB

2 Parallelogram ABCD with diagonals AC and BD intersecting at E is shown below.

Which statement must be true?1) BE ≅ CE2) ∠BAE ≅ ∠DCE3) AB ≅ BC4) ∠DAE ≅ ∠CBE

3 Which statement is true about every parallelogram?1) All four sides are congruent.2) The interior angles are all congruent.3) Two pairs of opposite sides are congruent.4) The diagonals are perpendicular to each other.

4 In parallelogram QRST, diagonal QS is drawn. Which statement must always be true?1) QRS is an isosceles triangle.2) STQ is an acute triangle.3) STQ ≅ QRS4) QS ≅ QT

5 Which statement is not always true about a parallelogram?1) The diagonals are congruent.2) The opposite sides are congruent.3) The opposite angles are congruent.4) The opposite sides are parallel.

6 In the accompanying diagram of parallelogram ABCD, m∠A = (2x + 10) and m∠B = 3x . Find the number of degrees in m∠B.

Regents Exam Questions G.CO.C.11: Parallelograms 2 Name: ________________________ www.jmap.org

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G.CO.C.11: Parallelograms 2

1 In the diagram below, parallelogram ABCD has diagonals AC and BD that intersect at point E.

Which expression is not always true?1) ∠DAE ≅ ∠BCE2) ∠DEC ≅ ∠BEA3) AC ≅ DB4) DE ≅ EB

2 Parallelogram ABCD with diagonals AC and BD intersecting at E is shown below.

Which statement must be true?1) BE ≅ CE2) ∠BAE ≅ ∠DCE3) AB ≅ BC4) ∠DAE ≅ ∠CBE

3 Which statement is true about every parallelogram?1) All four sides are congruent.2) The interior angles are all congruent.3) Two pairs of opposite sides are congruent.4) The diagonals are perpendicular to each other.

4 In parallelogram QRST, diagonal QS is drawn. Which statement must always be true?1) QRS is an isosceles triangle.2) STQ is an acute triangle.3) STQ ≅ QRS4) QS ≅ QT

5 Which statement is not always true about a parallelogram?1) The diagonals are congruent.2) The opposite sides are congruent.3) The opposite angles are congruent.4) The opposite sides are parallel.

6 In the accompanying diagram of parallelogram ABCD, m∠A = (2x + 10) and m∠B = 3x . Find the number of degrees in m∠B.

Name: ________________________________________________________ Date: _____________ Ms. Ayinde Geometry CC 4.3: Conditions of Parallelograms Objective: To determine what information is necessary to conclude a quadrilateral is a parallelogram. Do Now: Quietly and independently, check your homework with the answer key provided to you. Since a parallelogram is a quadrilateral, its interior angle sum and exterior angle sum are both ______________.

More specifically, a parallelogram is a quadrilateral with _____________ pairs of ________________________

sides parallel. Since both pairs of opposite sides are parallel, they are also __________________________. The

________________________ angles of parallelograms are congruent, while the _________________________

are supplementary. Lastly, the diagonals _________________ each other. Today we are going to be determine

what would be necessary to conclude that a quadrilateral is a parallelogram.

Using each diagram, list what you know about each quadrilateral.

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I know… Conclusion:

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I know…

3.

I know…

4.

I know…

Practice: Solve the following problems. Show your work when necessary.

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Regents Exam Questions G.CO.C.11: Parallelograms 1 Name: ________________________ www.jmap.org

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G.CO.C.11: Parallelograms 1

1 In quadrilateral BLUE shown below, BE ≅ UL.

Which information would be sufficient to prove quadrilateral BLUE is a parallelogram?1) BL ~ EU2) LU ~ BE3) BE ≅ BL4) LU ≅ EU

2 Quadrilateral ABCD with diagonals AC and BD is shown in the diagram below.

Which information is not enough to prove ABCD is a parallelogram?1) AB ≅ CD and AB ~ DC2) AB ≅ CD and BC ≅ DA3) AB ≅ CD and BC ~ AD4) AB ~ DC and BC ~ AD

3 Quadrilateral ABCD has diagonals AC and BD . Which information is not sufficient to prove ABCD is a parallelogram?1) AC and BD bisect each other.2) AB ≅ CD and BC ≅ AD3) AB ≅ CD and AB ~ CD4) AB ≅ CD and BC ~ AD

4 Parallelogram HAND is drawn below with diagonals HN and AD intersecting at S.

Which statement is always true?

1) AN = 12 AD

2) AS = 12 AD

3) ∠AHS ≅ ∠ANS4) ∠HDS ≅ ∠NDS

5 Quadrilateral MATH has both pairs of opposite sides congruent and parallel. Which statement about quadrilateral MATH is always true?1) MT ≅ AH2) MT⊥AH3) ∠MHT ≅ ∠ATH4) ∠MAT ≅ ∠MHT

6 In parallelogram ABCD shown below, the bisectors of ∠ABC and ∠DCB meet at E, a point on AD.

If m∠A = 68°, determine and state m∠BEC .

Regents Exam Questions G.CO.C.11: Parallelograms 1 Name: ________________________ www.jmap.org

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G.CO.C.11: Parallelograms 1

1 In quadrilateral BLUE shown below, BE ≅ UL.

Which information would be sufficient to prove quadrilateral BLUE is a parallelogram?1) BL ~ EU2) LU ~ BE3) BE ≅ BL4) LU ≅ EU

2 Quadrilateral ABCD with diagonals AC and BD is shown in the diagram below.

Which information is not enough to prove ABCD is a parallelogram?1) AB ≅ CD and AB ~ DC2) AB ≅ CD and BC ≅ DA3) AB ≅ CD and BC ~ AD4) AB ~ DC and BC ~ AD

3 Quadrilateral ABCD has diagonals AC and BD . Which information is not sufficient to prove ABCD is a parallelogram?1) AC and BD bisect each other.2) AB ≅ CD and BC ≅ AD3) AB ≅ CD and AB ~ CD4) AB ≅ CD and BC ~ AD

4 Parallelogram HAND is drawn below with diagonals HN and AD intersecting at S.

Which statement is always true?

1) AN = 12 AD

2) AS = 12 AD

3) ∠AHS ≅ ∠ANS4) ∠HDS ≅ ∠NDS

5 Quadrilateral MATH has both pairs of opposite sides congruent and parallel. Which statement about quadrilateral MATH is always true?1) MT ≅ AH2) MT⊥AH3) ∠MHT ≅ ∠ATH4) ∠MAT ≅ ∠MHT

6 In parallelogram ABCD shown below, the bisectors of ∠ABC and ∠DCB meet at E, a point on AD.

If m∠A = 68°, determine and state m∠BEC .

Regents Exam Questions G.CO.C.11: Parallelograms 1 Name: ________________________ www.jmap.org

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G.CO.C.11: Parallelograms 1

1 In quadrilateral BLUE shown below, BE ≅ UL.

Which information would be sufficient to prove quadrilateral BLUE is a parallelogram?1) BL ~ EU2) LU ~ BE3) BE ≅ BL4) LU ≅ EU

2 Quadrilateral ABCD with diagonals AC and BD is shown in the diagram below.

Which information is not enough to prove ABCD is a parallelogram?1) AB ≅ CD and AB ~ DC2) AB ≅ CD and BC ≅ DA3) AB ≅ CD and BC ~ AD4) AB ~ DC and BC ~ AD

3 Quadrilateral ABCD has diagonals AC and BD . Which information is not sufficient to prove ABCD is a parallelogram?1) AC and BD bisect each other.2) AB ≅ CD and BC ≅ AD3) AB ≅ CD and AB ~ CD4) AB ≅ CD and BC ~ AD

4 Parallelogram HAND is drawn below with diagonals HN and AD intersecting at S.

Which statement is always true?

1) AN = 12 AD

2) AS = 12 AD

3) ∠AHS ≅ ∠ANS4) ∠HDS ≅ ∠NDS

5 Quadrilateral MATH has both pairs of opposite sides congruent and parallel. Which statement about quadrilateral MATH is always true?1) MT ≅ AH2) MT⊥AH3) ∠MHT ≅ ∠ATH4) ∠MAT ≅ ∠MHT

6 In parallelogram ABCD shown below, the bisectors of ∠ABC and ∠DCB meet at E, a point on AD.

If m∠A = 68°, determine and state m∠BEC .

Regents Exam Questions G.CO.C.11: Parallelograms 1 Name: ________________________ www.jmap.org

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G.CO.C.11: Parallelograms 1

1 In quadrilateral BLUE shown below, BE ≅ UL.

Which information would be sufficient to prove quadrilateral BLUE is a parallelogram?1) BL ~ EU2) LU ~ BE3) BE ≅ BL4) LU ≅ EU

2 Quadrilateral ABCD with diagonals AC and BD is shown in the diagram below.

Which information is not enough to prove ABCD is a parallelogram?1) AB ≅ CD and AB ~ DC2) AB ≅ CD and BC ≅ DA3) AB ≅ CD and BC ~ AD4) AB ~ DC and BC ~ AD

3 Quadrilateral ABCD has diagonals AC and BD . Which information is not sufficient to prove ABCD is a parallelogram?1) AC and BD bisect each other.2) AB ≅ CD and BC ≅ AD3) AB ≅ CD and AB ~ CD4) AB ≅ CD and BC ~ AD

4 Parallelogram HAND is drawn below with diagonals HN and AD intersecting at S.

Which statement is always true?

1) AN = 12 AD

2) AS = 12 AD

3) ∠AHS ≅ ∠ANS4) ∠HDS ≅ ∠NDS

5 Quadrilateral MATH has both pairs of opposite sides congruent and parallel. Which statement about quadrilateral MATH is always true?1) MT ≅ AH2) MT⊥AH3) ∠MHT ≅ ∠ATH4) ∠MAT ≅ ∠MHT

6 In parallelogram ABCD shown below, the bisectors of ∠ABC and ∠DCB meet at E, a point on AD.

If m∠A = 68°, determine and state m∠BEC .

Regents Exam Questions G.CO.C.11: Parallelograms 1 Name: ________________________ www.jmap.org

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G.CO.C.11: Parallelograms 1

1 In quadrilateral BLUE shown below, BE ≅ UL.

Which information would be sufficient to prove quadrilateral BLUE is a parallelogram?1) BL ~ EU2) LU ~ BE3) BE ≅ BL4) LU ≅ EU

2 Quadrilateral ABCD with diagonals AC and BD is shown in the diagram below.

Which information is not enough to prove ABCD is a parallelogram?1) AB ≅ CD and AB ~ DC2) AB ≅ CD and BC ≅ DA3) AB ≅ CD and BC ~ AD4) AB ~ DC and BC ~ AD

3 Quadrilateral ABCD has diagonals AC and BD . Which information is not sufficient to prove ABCD is a parallelogram?1) AC and BD bisect each other.2) AB ≅ CD and BC ≅ AD3) AB ≅ CD and AB ~ CD4) AB ≅ CD and BC ~ AD

4 Parallelogram HAND is drawn below with diagonals HN and AD intersecting at S.

Which statement is always true?

1) AN = 12 AD

2) AS = 12 AD

3) ∠AHS ≅ ∠ANS4) ∠HDS ≅ ∠NDS

5 Quadrilateral MATH has both pairs of opposite sides congruent and parallel. Which statement about quadrilateral MATH is always true?1) MT ≅ AH2) MT⊥AH3) ∠MHT ≅ ∠ATH4) ∠MAT ≅ ∠MHT

6 In parallelogram ABCD shown below, the bisectors of ∠ABC and ∠DCB meet at E, a point on AD.

If m∠A = 68°, determine and state m∠BEC .

Regents Exam Questions G.CO.C.11: Parallelograms 1 Name: ________________________ www.jmap.org

1

G.CO.C.11: Parallelograms 1

1 In quadrilateral BLUE shown below, BE ≅ UL.

Which information would be sufficient to prove quadrilateral BLUE is a parallelogram?1) BL ~ EU2) LU ~ BE3) BE ≅ BL4) LU ≅ EU

2 Quadrilateral ABCD with diagonals AC and BD is shown in the diagram below.

Which information is not enough to prove ABCD is a parallelogram?1) AB ≅ CD and AB ~ DC2) AB ≅ CD and BC ≅ DA3) AB ≅ CD and BC ~ AD4) AB ~ DC and BC ~ AD

3 Quadrilateral ABCD has diagonals AC and BD . Which information is not sufficient to prove ABCD is a parallelogram?1) AC and BD bisect each other.2) AB ≅ CD and BC ≅ AD3) AB ≅ CD and AB ~ CD4) AB ≅ CD and BC ~ AD

4 Parallelogram HAND is drawn below with diagonals HN and AD intersecting at S.

Which statement is always true?

1) AN = 12 AD

2) AS = 12 AD

3) ∠AHS ≅ ∠ANS4) ∠HDS ≅ ∠NDS

5 Quadrilateral MATH has both pairs of opposite sides congruent and parallel. Which statement about quadrilateral MATH is always true?1) MT ≅ AH2) MT⊥AH3) ∠MHT ≅ ∠ATH4) ∠MAT ≅ ∠MHT

6 In parallelogram ABCD shown below, the bisectors of ∠ABC and ∠DCB meet at E, a point on AD.

If m∠A = 68°, determine and state m∠BEC .