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Grade 10 · Math · Geometry

10th grade Angle and parallel-line proofs: fill in the missing reason worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

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Angle and parallel-line proofs: fill in the missing reason

Grade 10 Math Worksheet - Building Confidence

NameDate

Circle the best answer.

  1. Read this first

    Use this

    Given: lines CG and DH cross at Q. Prove: ∠CQH ≅ ∠GQD. Ladder: 1. Lines CG and DH cross at Q -- Given; 2. ∠CQH ≅ ∠GQD -- ?.

  2. Ari opens a pair of scissors, and the blades lie along lines CG and DH. Which reason fills the blank?

    • Given
    • Angle addition postulate
    • Vertical angles theorem
    • Linear pair postulate

  3. Bo builds a kite whose two sticks lie along lines CG and DH. Which reason fills the blank?

    • Given
    • Linear pair postulate
    • Vertical angles theorem
    • Definition of complementary angles

  4. Use this

    Given: UV ∥ WY. Prove: ∠VSQ ≅ ∠SQW. Ladder: 1. UV ∥ WY -- Given; 2. ∠VSQ ≅ ∠SQW -- ?.

  5. Esme draws train rails UV and WY, crossed by road HD. Which reason fills the blank?

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

  6. Jun sees two stripes UV and WY on a rug, crossed by a seam HD. Which reason fills the blank?

    • Given
    • Alternate exterior angles theorem
    • Converse of the corresponding angles postulate
    • Corresponding angles postulate

  7. Sketch, not to scale

    Line UV above line WY (U and W on the left), crossed by line HD at S on UV and at Q on WY (H at the top, D at the bottom). Marked: ∠HSU and ∠SQW with one arc each (no parallel arrows). Given: ∠HSU ≅ ∠SQW. Prove: ∠VSQ ≅ ∠SQW. Ladder: 1. ∠HSU ≅ ∠SQW — Given; 2. ∠VSQ ≅ ∠HSU — Vertical angles theorem; 3. ∠VSQ ≅ ∠SQW — ?.

  8. Kira sketches window bars UV and WY, crossed by a brace HD. Which reason fills the blank?

    • Alternate interior angles theorem
    • Symmetric property
    • Transitive property
    • Given

  9. Sketch, not to scale

    Line UV above line WY (U and W on the left), crossed by line HD at S on UV and at Q on WY (H at the top, D at the bottom). Marked: ∠USQ and ∠WQD with one arc each (no parallel arrows). Given: ∠USQ ≅ ∠WQD. Prove: ∠HSV ≅ ∠WQD. Ladder: 1. ∠USQ ≅ ∠WQD — Given; 2. ∠HSV ≅ ∠USQ — Vertical angles theorem; 3. ∠HSV ≅ ∠WQD — ?.

  10. Luz traces streets UV and WY on a map, crossed by avenue HD. Which reason fills the blank?

    • Alternate exterior angles theorem
    • Reflexive property
    • Transitive property
    • Given

  11. Use this

    Given: ∠USQ ≅ ∠SQY. Prove: UV ∥ WY. Ladder: 1. ∠USQ ≅ ∠SQY -- Given; 2. ∠HSV ≅ ∠USQ -- Vertical angles theorem; 3. ∠HSV ≅ ∠SQY -- Transitive property; 4. UV ∥ WY -- ?.

  12. Pia checks that train rails UV and WY never meet, using road HD. Which reason fills the blank?

    • Given
    • Converse of the corresponding angles postulate
    • Corresponding angles postulate
    • Converse of the alternate exterior angles theorem

  13. Use this

    Given: ∠SQY ≅ ∠HSV. Prove: ∠WQD ≅ ∠HSV. Ladder: 1. ∠SQY ≅ ∠HSV -- Given; 2. ? -- Vertical angles theorem; 3. ∠WQD ≅ ∠HSV -- Transitive property.

  14. Milo draws a door's edges UV and WY, crossed by a ribbon HD. Which statement fills the blank?

    • ∠WQD ≅ ∠HSV
    • ∠WQD ≅ ∠YQD
    • ∠HSV ≅ ∠SQY
    • ∠WQD ≅ ∠SQY

  15. Tala draws tent poles UV and WY, joined by a cord HD. Which statement fills the blank?

    • ∠WQD ≅ ∠HSV
    • ∠USQ ≅ ∠WQD
    • UV ∥ WY
    • ∠USQ ≅ ∠SQY

  16. Use this

    Given: ∠YQD ≅ ∠HSU. Prove: UV ∥ WY. Ladder: 1. ∠YQD ≅ ∠HSU -- Given; 2. ∠SQW ≅ ∠YQD -- Vertical angles theorem; 3. ? -- Transitive property; 4. UV ∥ WY -- Converse of the corresponding angles postulate.

  17. Zee sews quilt stripes UV and WY, crossed by a stitch line HD. Which statement fills the blank?

    • ∠SQW ≅ ∠SQY
    • ∠SQW ≅ ∠HSU
    • UV ∥ WY
    • ∠HSU ≅ ∠YQD
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10th grade Angle and parallel-line proofs: fill in the missing reason worksheet – printable
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About this worksheet

Angle and parallel-line proofs: fill in the missing 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 angles and parallel lines.
  • I can tell a theorem from its converse: parallel lines give angles, and angles give parallel lines.
  • I can choose the statement that a reason gives, and spot a rung that skips ahead.

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.

linear pair: Two angles that share a side and together make a straight line.

vertical angles: Opposite angles where two lines cross.

supplementary / complementary: Two angles adding to 180° / adding to 90°.

transitive property: If a matches b and b matches c, then a matches c.

substitution property: Swap a value for an equal one inside a statement.

Common mistakes

Your child gave the rule for the wrong kind of angle pair. Point to each angle on the drawing and say which corner of each crossing it sits in.

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 named the converse of a theorem when the theorem itself was needed. The theorem goes from parallel lines to equal angles; its converse goes from equal angles to parallel lines.

What to say

Ask: which fact do we already have?

Questions parents ask

What is the most common mistake with angle and parallel-line proofs: fill in the missing reason?

Your child gave the rule for the wrong kind of angle pair. Point to each angle on the drawing and say which corner of each crossing it sits in.

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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