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

Answer Key - Grade 10 Math Worksheet - Building Confidence

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

1. 1.

   Esme marks the facts known about a paper shape DFGH. Do the marks prove that DFGH is a parallelogram?

   • Yes: all four sides are equal.
   • Yes: both pairs of opposite sides are equal.
   • No: no sides are marked parallel.
   • No: it also needs a right angle.
2. 2.

   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.
   • Yes: one pair is parallel and the other pair is equal.
   • No: an isosceles trapezoid has these marks too.
   • No: a parallelogram needs four right angles.
3. 3.

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

   • No: the diagonals must also be equal.
   • No: the diagonals must cross at right angles.
   • Yes: the diagonals cut each other in half.
   • Yes: one pair of sides is parallel.
4. 4.

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

   • No: no angles are marked.
   • Yes: it has two pairs of equal sides.
   • Yes: both pairs of opposite sides are equal.
   • No: a kite has these marks too.
5. 5.

   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?

   7
6. 6.

   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?

   10
7. 7.

   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
8. 8.

   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?

   6
9. 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?

   6
10. 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?

    7