Mathematics 9 Parallelograms: Properties and Naming
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Questions and Answers

Which of the following is sufficient to guarantee that a quadrilateral is a parallelogram?

  • The diagonals are perpendicular
  • The diagonals bisect each other
  • Two consecutive angles are congruent
  • Opposite sides are equal in length (correct)

    • What values of x and y guarantee that Quadrilateral ABCD is a parallelogram?

  • x = 320, y = 640
  • x = 640, y = 1160
  • x = 640, y = 640 (correct)
  • x = 320, y = 1160

    • In the same figure above, If AD = 2x – 10 cm and BC = x + 30 cm, then BC =

  • 50 cm
  • 60 cm
  • 70 cm (correct)
  • 80 cm

    • Quadrilateral ABCD is a parallelogram. If m∠B = (x + 40)° and m∠D = (2x + 20)°, what is m∠B?

    <p>60°</p> Signup and view all the answers

    Quadrilateral ABCD is a parallelogram. If m∠A = (3x – 10)° and m∠D = (2x + 40)°, what is m∠A?

    <p>70°</p> Signup and view all the answers

    Which of the following statements is true about parallelograms?

    <p>Any two opposite sides of a parallelogram are equal in length.</p> Signup and view all the answers

    What happens if one pair of opposite sides of a quadrilateral are parallel and congruent?

    <p>It becomes a parallelogram.</p> Signup and view all the answers

    What are the conditions for a quadrilateral to be classified as a parallelogram?

    <p>Only one pair of opposite sides are parallel and congruent.</p> Signup and view all the answers

    In a parallelogram, what can be said about any two consecutive angles?

    <p>They add up to 180 degrees.</p> Signup and view all the answers

    What is true about the naming convention of parallelograms?

    <p>The naming convention can start at any vertex in any order.</p> Signup and view all the answers

    In a parallelogram, what is true about any two consecutive angles?

    <p>They are supplementary</p> Signup and view all the answers

    If ̅̅̅̅ ≅ ̅̅̅ and ̅̅̅̅ // ̅̅̅ , then what can be concluded about the quadrilateral LIVE?

    <p>It is a parallelogram</p> Signup and view all the answers

    What happens if one pair of opposite sides of a quadrilateral are parallel and congruent?

    <p>The quadrilateral may be a parallelogram</p> Signup and view all the answers

    In a parallelogram, what can be said about the diagonals?

    <p>They bisect each other</p> Signup and view all the answers

    Which of the following conditions is sufficient to guarantee that a quadrilateral is a parallelogram?

    <p>One pair of opposite sides are parallel and congruent</p> Signup and view all the answers

    If m̅̅̅̅ = 13 cm, then m̅̅̅̅ = _____

    <p>3x - 5 cm</p> Signup and view all the answers

    Quadrilateral ABCD is a parallelogram. If m∠A = (3x – 10)° and m∠D = (2x + 40)°, what is m∠A?

    <p>80°</p> Signup and view all the answers

    What values of x and y guarantee that Quadrilateral ABCD is a parallelogram?

    <p>x = 640, y = 1160</p> Signup and view all the answers

    In the same figure above, If AD = 2x – 10cm and BC = x + 30 cm, then BC =

    <p>70 cm</p> Signup and view all the answers

    Which of the following is sufficient to guarantee that a quadrilateral is a parallelogram?

    <p>Opposite sides are parallel and congruent</p> Signup and view all the answers

    Study Notes

    Conditions for a Parallelogram

    • A quadrilateral is a parallelogram if one pair of opposite sides are parallel and congruent.
    • A quadrilateral is a parallelogram if both pairs of opposite angles are equal.
    • A quadrilateral is a parallelogram if both pairs of opposite sides are equal.
    • A quadrilateral is a parallelogram if the diagonals bisect each other.

    Properties of Parallelograms

    • In a parallelogram, any two consecutive angles are supplementary (add up to 180°).
    • In a parallelogram, the diagonals bisect each other.
    • In a parallelogram, opposite sides are equal and parallel.

    Naming Convention of Parallelograms

    • The naming convention of parallelograms is to name them in alphabetical order.

    Consecutive Angles in Parallelograms

    • In a parallelogram, any two consecutive angles are supplementary (add up to 180°).

    Diagonals in Parallelograms

    • In a parallelogram, the diagonals bisect each other.

    Quadrilateral ABCD

    • Quadrilateral ABCD is a parallelogram if AD = 2x – 10 cm and BC = x + 30 cm.
    • Quadrilateral ABCD is a parallelogram if m∠A = (3x – 10)° and m∠D = (2x + 40)°.

    Example Problems

    • If m̅̅̅̅ ≅ ̅̅̅ and ̅̅̅̅ // ̅̅̅, then the quadrilateral LIVE is a parallelogram.
    • If m̅̅̅̅ = 13 cm, then m̅̅̅̅ = ?.

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    Description

    Learn about the definition of a parallelogram as a quadrilateral with two pairs of parallel sides, and the rules for naming a parallelogram. Explore the properties of a parallelogram, including the congruence of opposite sides.

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