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Grade 10 · Math · Geometry

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 - Challenge Me

NameDate

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

  1. Esme's window is parallelogram DFGH, with diagonals crossing at Q. DQ = (3x − 5) cm and FH = (2x + 26) cm. How long is FH if it is a rectangle, in cm?

  2. Jun's picture frame is parallelogram DFGH, with diagonals crossing at Q. DQ = (3x − 7) cm and FH = (2x + 10) cm. How long is FH if it is a rectangle, in cm?

  3. Kira's door is parallelogram DFGH, with diagonals crossing at Q. DQ = (4x − 9) cm and FH = (2x + 24) cm. How long is FH if it is a rectangle, in cm?

  4. Luz's table top is parallelogram DFGH, with diagonals crossing at Q. DQ = (3x − 2) cm and FH = (2x + 20) cm. How long is FH if it is a rectangle, in cm?

  5. Milo's craft frame DFGH is a parallelogram. DF = (3x − 4) cm and FG = (x + 8) cm. What is its perimeter when DFGH is a rhombus, in cm?

  6. Noah's tile DFGH is a parallelogram. DF = (6x + 2) cm and FG = (2x + 22) cm. What is its perimeter when DFGH is a rhombus, in cm?

  7. Ren's sticker DFGH is a parallelogram. DF = (2x + 7) cm and FG = (4x − 5) cm. What is its perimeter when DFGH is a rhombus, in cm?

  9. Zee hears a claim: "If a quadrilateral's diagonals cross at right angles, it is a rhombus." Which shape shows the claim is false?

    • A square
    • An isosceles trapezoid
    • A kite with two short and two long sides
    • A long rectangle

  10. Ari hears a claim: "If one pair of opposite sides is parallel and the other pair is equal, it is a parallelogram." Which shape shows the claim is false?

    Use the picture in question 8.

    • A rectangle
    • A rhombus
    • A kite
    • An isosceles trapezoid

  11. Bo hears a claim: "If a quadrilateral has four equal sides, it is a square." Which shape shows the claim is false?

    Use the picture in question 8.

    • A long rectangle
    • A square
    • A rhombus with no right angle
    • A kite
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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.

More geometry

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