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10th grade Is this quadrilateral a parallelogram, rectangle, rhombus or square? Which facts are enough? worksheet

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Is this quadrilateral a parallelogram, rectangle, rhombus or square? Which facts are enough?

Grade 10 Math Worksheet

NameDate

Circle the best answer, or write your answer on the line.

  2. Esme has four cards, each with facts about DFGH. Which card proves that DFGH is a parallelogram?

    • DF = DH and GF = GH
    • DF ∥ HG and DF = HG
    • DF ∥ HG and FG = DH
    • DF = HG only

  3. Jun has four cards, each with facts about DFGH. Which card proves that DFGH is a parallelogram?

    Use the picture in question 1.

    • DG ⊥ FH
    • DF ∥ HG only
    • ∠D = ∠G and ∠F = ∠H
    • DG = FH

  4. Kira has four cards, each with facts about DFGH. Which card proves that DFGH is a parallelogram?

    Use the picture in question 1.

    • ∠F = ∠H only
    • FG = DH only
    • DF ∥ HG, ∠D = ∠F and ∠G = ∠H
    • DQ = QG and FQ = QH

  5. Luz has four cards, each with facts about DFGH. Which card proves that DFGH is a parallelogram?

    Use the picture in question 1.

    • DF ∥ HG and DG = FH
    • DG ⊥ FH and FQ = QH
    • DF ∥ HG only
    • DF = HG and FG = DH

  6. Milo knows DFGH is a parallelogram. Its diagonals are equal: DG = FH. Which name fits DFGH best?

    • Just a parallelogram
    • Rectangle
    • Square
    • Rhombus

  7. Noah knows DFGH is a parallelogram. Its diagonals cross at right angles. Which name fits DFGH best?

    • Rhombus
    • Just a parallelogram
    • Square
    • Rectangle

  8. Ren knows DFGH is a parallelogram. Its diagonals are equal and cross at right angles. Which name fits DFGH best?

    • Just a parallelogram
    • Square
    • Rhombus
    • Rectangle

  9. Zee's garden bed DFGH has DF ∥ HG. m∠D = (4x − 8)° and m∠F = (2x + 20)°. What value of x makes DH ∥ FG, so DFGH is a parallelogram?

  10. Ari's window DFGH has DF ∥ HG. m∠D = (5x − 15)° and m∠F = (3x + 11)°. What value of x makes DH ∥ FG, so DFGH is a parallelogram?

  11. Bo's tile DFGH has DF ∥ HG. m∠D = (2x + 14)° and m∠F = (4x − 8)°. What value of x makes DH ∥ FG, so DFGH is a parallelogram?

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10th grade Is this quadrilateral a parallelogram, rectangle, rhombus or square? Which facts are enough? worksheet – printable
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About this worksheet

Is it a parallelogram? Which facts are enough. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can say whether the marked facts are enough to prove that a quadrilateral is a parallelogram.
  • I can name an isosceles trapezoid or a kite that has the same facts when they are not enough.
  • I can find the value of x that makes a quadrilateral a parallelogram, rectangle or rhombus.

Standard: G-CO.C.11 (converses; related)

Words to know

enough (to prove): The facts force the shape; no other shape can have them.

test: A set of facts that is always enough, such as both pairs of opposite sides equal.

counterexample: A shape that has the "if" facts but is not the claimed shape.

isosceles trapezoid: One pair of parallel sides and equal legs; it is not a parallelogram.

kite: Two pairs of equal sides that meet; it is not a parallelogram.

Common mistakes

Your child asked for more facts than a parallelogram needs. Both pairs of opposite sides equal, or diagonals that cut each other in half, is already enough. A right angle or equal diagonals would make a rectangle.

Your child gave a reason that the marks do not show. A proof can use only the facts that are given. Point to the mark that backs each reason.

Your child said the marks prove a parallelogram, but an isosceles trapezoid or a kite has the same marks. Try to draw a shape that has the marks and is not a parallelogram.

Questions parents ask

What is the most common mistake with is this quadrilateral a parallelogram, rectangle, rhombus or square? which facts are enough??

Your child asked for more facts than a parallelogram needs. Both pairs of opposite sides equal, or diagonals that cut each other in half, is already enough. A right angle or equal diagonals would make a rectangle.

Are these 10th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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