Quadrilateral proofs: fill in the missing step or reason

Grade 10 Math Worksheet - Building Confidence

Circle the best answer.

1. 1.

   Noah sketches a slanted door panel DFGH, a parallelogram. Which reason fills the blank?

   • Definition of parallelogram
   • Given
   • Reflexive property
   • Parallelogram opposite sides theorem
2. 2.

   Pia cuts a parallelogram tile DFGH for a floor pattern. Which reason fills the blank?

   • Parallelogram opposite angles theorem
   • Definition of rectangle
   • Given
   • Parallelogram consecutive angles theorem
3. 3.

   Ren builds a parallelogram frame DFGH with two sticks crossing at Q. Which reason fills the blank?

   • Given
   • Parallelogram diagonals theorem
   • Definition of midpoint
   • Rectangle diagonals theorem
4. 4.

   Tala flies a rhombus-shaped kite DFGH whose sticks cross at Q. Which reason fills the blank?

   • Given
   • Rectangle diagonals theorem
   • Parallelogram diagonals theorem
   • Rhombus diagonals theorem
5. 5.

   Zee braces a rectangle door DFGH with two boards from corner to corner. Which reason fills the blank?

   • Parallelogram diagonals theorem
   • Reflexive property
   • Rectangle diagonals theorem
   • Rhombus diagonals theorem
6. 6.

   Ari lays a parallelogram rug DFGH on a floor. Which reason fills the blank?

   • Parallelogram opposite angles theorem
   • Definition of rectangle
   • Parallelogram consecutive angles theorem
   • Given
7. 7.

   Bo sews a parallelogram quilt patch DFGH. Which reason fills the blank?

   • Midsegment theorem
   • Parallelogram consecutive angles theorem
   • Parallelogram opposite angles theorem
   • Definition of rectangle
8. 8.

   Esme ties string across a parallelogram box lid DFGH, corner to corner. Which statement fills the blank?

   • DQ ≅ FQ and QG ≅ QH
   • DQ ≅ QG and FQ ≅ QH
   • Q is the midpoint of DG
   • DG ≅ FH
9. 9.

   Kira draws the top of a parallelogram table DFGH. Which statement fills the blank?

   • DF ≅ FG
   • ∠DFG ≅ ∠GHD
   • m∠DFG = m∠GHD
   • ∠DFG ≅ ∠FGH
10. 10.

    Luz folds a parallelogram flap DFGH on an envelope. Which statement fills the blank?

    • FG ∥ GH
    • FG ≅ HD
    • FG = HD
    • FG ≅ GH