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10th grade Quadrilateral proofs: fill in the missing step or reason worksheet

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Quadrilateral proofs: fill in the missing step or reason

Grade 10 Math Worksheet

NameDate

Circle the best answer.

  1. Read this first

    Use this

    Given: DFGH is a parallelogram. Prove: DF ≅ GH. Ladder: 1. DFGH is a parallelogram -- Given; 2. DF ∥ HG and DH ∥ FG -- Definition of parallelogram; 3. ∠FDG ≅ ∠HGD -- Alternate interior angles theorem; 4. ∠HDG ≅ ∠FGD -- Alternate interior angles theorem; 5. DG ≅ DG -- Reflexive property; 6. triangle DFG ≅ triangle GHD -- ASA; 7. DF ≅ GH -- ?.

  2. Milo proves the parallelogram opposite sides theorem on a window frame DFGH, using diagonal DG. Which reason fills the blank?

    • Parallelogram opposite sides theorem
    • ASA
    • Given
    • CPCTC

  3. Use this

    Given: DFGH is a parallelogram. Prove: GH ≅ DF. Ladder: 1. DFGH is a parallelogram -- Given; 2. DF ∥ HG and DH ∥ FG -- Definition of parallelogram; 3. ∠DFH ≅ ∠GHF -- Alternate interior angles theorem; 4. ∠GFH ≅ ∠DHF -- Alternate interior angles theorem; 5. FH ≅ FH -- Reflexive property; 6. triangle FGH ≅ triangle HDF -- ASA; 7. GH ≅ DF -- ?.

  4. Noah proves the parallelogram opposite sides theorem on a rug DFGH, using diagonal FH. Which reason fills the blank?

    • Parallelogram opposite sides theorem
    • ASA
    • CPCTC
    • Given

  5. Use this

    Given: DFGH is a parallelogram. Prove: ∠DFG ≅ ∠GHD. Ladder: 1. DFGH is a parallelogram -- Given; 2. DF ∥ HG and DH ∥ FG -- Definition of parallelogram; 3. ∠FDG ≅ ∠HGD -- ?; 4. ∠HDG ≅ ∠FGD -- Alternate interior angles theorem; 5. DG ≅ DG -- Reflexive property; 6. triangle DFG ≅ triangle GHD -- ASA; 7. ∠DFG ≅ ∠GHD -- CPCTC.

  6. Pia proves the parallelogram opposite angles theorem on a tile DFGH, using diagonal DG. Which reason fills the blank?

    • Corresponding angles postulate
    • Converse of the alternate interior angles theorem
    • CPCTC
    • Alternate interior angles theorem

  7. Use this

    Given: DFGH is a parallelogram. Prove: ∠FGH ≅ ∠HDF. Ladder: 1. DFGH is a parallelogram -- Given; 2. DF ∥ HG and DH ∥ FG -- Definition of parallelogram; 3. ∠DFH ≅ ∠GHF -- Alternate interior angles theorem; 4. ∠GFH ≅ ∠DHF -- ?; 5. FH ≅ FH -- Reflexive property; 6. triangle FGH ≅ triangle HDF -- ASA; 7. ∠FGH ≅ ∠HDF -- CPCTC.

  8. Ren proves the parallelogram opposite angles theorem on a table top DFGH, using diagonal FH. Which reason fills the blank?

    • Alternate exterior angles theorem
    • Alternate interior angles theorem
    • CPCTC
    • Converse of the alternate interior angles theorem

  9. Use this

    Given: DFGH is a parallelogram. Prove: FG ≅ HD. Ladder: 1. DFGH is a parallelogram -- Given; 2. DF ∥ HG and DH ∥ FG -- Definition of parallelogram; 3. ∠FDG ≅ ∠HGD -- Alternate interior angles theorem; 4. ∠HDG ≅ ∠FGD -- Alternate interior angles theorem; 5. DG ≅ DG -- Reflexive property; 6. triangle DFG ≅ triangle GHD -- ?; 7. FG ≅ HD -- CPCTC.

  10. Tala proves that FG ≅ HD on a parallelogram door panel DFGH, using diagonal DG. Which reason fills the blank?

    • SAS
    • CPCTC
    • ASA
    • Definition of parallelogram

  11. Use this

    Given: DFGH is a parallelogram. Prove: FG ≅ HD. Ladder: 1. DFGH is a parallelogram -- Given; 2. DF ∥ HG and DH ∥ FG -- Definition of parallelogram; 3. ∠DFH ≅ ∠GHF -- Alternate interior angles theorem; 4. ∠GFH ≅ ∠DHF -- Alternate interior angles theorem; 5. FH ≅ FH -- Reflexive property; 6. triangle FGH ≅ triangle HDF -- ?; 7. FG ≅ HD -- CPCTC.

  12. Zee proves that FG ≅ HD on a parallelogram quilt patch DFGH, using diagonal FH. Which reason fills the blank?

    • SSS
    • SAS
    • ASA
    • Reflexive property

  13. Use this

    Given: DFGH is a rectangle. Prove: DG ≅ FH. Ladder: 1. DFGH is a rectangle -- Given; 2. DFGH is a parallelogram, and ∠DHG and ∠FGH are right angles -- Definition of rectangle; 3. ? -- Right angles congruence theorem; 4. DH ≅ FG -- Parallelogram opposite sides theorem; 5. HG ≅ HG -- Reflexive property; 6. triangle DHG ≅ triangle FGH -- SAS; 7. DG ≅ FH -- CPCTC.

  14. Bo proves that the braces of a rectangle door DFGH are equal, using the top edge HG. Which statement fills the blank?

    • ∠DHG ≅ ∠HGD
    • DH ≅ FG
    • DG ≅ FH
    • ∠DHG ≅ ∠FGH

  15. Esme proves that the diagonals of a rectangle book cover DFGH are equal, using the left edge DH. Which statement fills the blank?

    • FH ≅ GD
    • △FDH ≅ △FGH
    • △FDH ≅ △DHG
    • △FDH ≅ △GHD

  16. Jun proves that the diagonals of a rectangle box lid DFGH are equal, using the right edge FG. Which statement fills the blank?

    • △DFG ≅ △GFH
    • DG ≅ HF
    • △DFG ≅ △FGH
    • △DFG ≅ △HGF

  17. Use this

    Given: DFGH is a parallelogram. Prove: HQ ≅ FQ. Ladder: 1. DFGH is a parallelogram -- Given; 2. DH ∥ FG -- Definition of parallelogram; 3. DH ≅ FG -- Parallelogram opposite sides theorem; 4. ? -- Alternate interior angles theorem; 5. ∠DHQ ≅ ∠GFQ -- Alternate interior angles theorem; 6. triangle DHQ ≅ triangle GFQ -- ASA; 7. HQ ≅ FQ -- CPCTC.

  18. Luz proves that the folds of a parallelogram paper DFGH cut each other in half at Q. Which statement fills the blank?

    • ∠HDQ ≅ ∠FGQ
    • HQ ≅ FQ
    • ∠HDQ ≅ ∠QDF
    • ∠HDQ ≅ ∠DFQ
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10th grade Quadrilateral proofs: fill in the missing step or reason worksheet – printable
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About this worksheet

Quadrilateral proofs: fill in the missing step or reason. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can name the reason for each step of a proof about a parallelogram, rectangle or rhombus.
  • I can tell which facts belong to every parallelogram and which only to a rectangle or rhombus.
  • I can use congruent triangles inside a quadrilateral, then CPCTC.

Words to know

rung: One line of the proof: a statement with its reason beside it.

Given / Prove: Given: the facts we start with. Prove: the statement the last rung must reach.

converse: The if-then turned around; it is a different statement, true or not.

parallelogram: A quadrilateral with both pairs of opposite sides parallel.

rectangle / rhombus: A parallelogram with four right angles / with four congruent sides.

opposite / next-door angles: Angles across the shape / angles that share a side.

right angles congruence theorem: All right angles are congruent.

linear pair perpendicular theorem: Two lines making a congruent linear pair are perpendicular.

Common mistakes

Your child wrote "Given" for the statement the proof is trying to reach. Only the facts on the Given line are given. Cover the Prove line and ask what is known.

Your child mixed up two facts: the definition of a parallelogram gives parallel opposite sides, and a theorem gives congruent (equal) opposite sides.

Your child used a fact that only a rectangle has, on a shape known only to be a parallelogram. Draw a leaning parallelogram and check whether the fact still holds.

Questions parents ask

What is the most common mistake with quadrilateral proofs: fill in the missing step or reason?

Your child wrote "Given" for the statement the proof is trying to reach. Only the facts on the Given line are given. Cover the Prove line and ask what is known.

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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