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Grade 10 · Math · Geometry

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

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

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

Grade 10 Math Worksheet - Building Confidence

NameDate

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

  1. Jun marks the facts known about a lamp shade outline DFGH. Do the marks prove that DFGH is a parallelogram?

    • Yes: both pairs of opposite sides are equal.
    • No: a parallelogram needs four right angles.
    • Yes: one pair is parallel and the other pair is equal.
    • No: an isosceles trapezoid has these marks too.

  2. Kira builds a frame DFGH from two sticks that cross at Q. Do the marks prove that DFGH is a parallelogram?

    • Yes: the diagonals cut each other in half.
    • No: the diagonals must also be equal.
    • No: the diagonals must cross at right angles.
    • Yes: one pair of sides is parallel.

  3. Luz marks the facts known about a kite-maker's sketch DFGH. Do the marks prove that DFGH is a parallelogram?

    • Yes: it has two pairs of equal sides.
    • No: a kite has these marks too.
    • Yes: both pairs of opposite sides are equal.
    • No: no angles are marked.

  4. Milo's picture frame is DFGH, with FG = DH = 9 cm. DF = (2x + 4) cm and GH = 18 cm. What value of x makes DFGH a parallelogram?

  5. Noah's garden bed is DFGH, with FG = DH = 13 cm. DF = (3x − 5) cm and GH = 25 cm. What value of x makes DFGH a parallelogram?

  6. Pia's window is DFGH, with FG = DH = 12 cm. DF = (4x + 2) cm and GH = 30 cm. What value of x makes DFGH a parallelogram?

  7. Tala's craft frame DFGH has diagonals meeting at Q; FQ = QH = 10 cm. DQ = (2x + 3) cm and QG = (4x − 9) cm. Which x makes it a parallelogram?

  8. Zee's picture frame DFGH has diagonals meeting at Q; FQ = QH = 16 cm. DQ = (5x − 6) cm and QG = (3x + 8) cm. Which x makes it a parallelogram?

  9. Ari's window DFGH has diagonals meeting at Q; FQ = QH = 21 cm. DQ = (4x + 1) cm and QG = (2x + 13) cm. Which x makes it a parallelogram?

  10. Bo's garden gate DFGH has diagonals meeting at Q; FQ = QH = 19 cm. DQ = (6x − 5) cm and QG = (2x + 23) cm. Which x makes it 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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