Grade 10 · Math · Geometry

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

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

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Quadrilateral proofs: fill in the missing step or reason

Grade 10 Math Worksheet - Building Confidence

NameDate

Circle the best answer.

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.
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.
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.
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.
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.
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.
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.
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.
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.
Luz folds a parallelogram flap DFGH on an envelope. Which statement fills the blank?
- FG ∥ GH
- FG ≅ HD
- FG = HD
- FG ≅ GH

10th grade Quadrilateral proofs: fill in the missing step or reason worksheet – printable — Print: 1 2 3 4 5 6

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.

More geometry

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