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Grade 10 · Math · Geometry

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

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

Grade 10 Math Worksheet

NameDate

Circle the best answer.

  1. Read this first

    Use this

    Ladder: 1. Lines CG and DH cross at Q -- Given; 2. ∠CQH and ∠HQG are supplementary -- Linear pair postulate; 3. ∠GQD and ∠HQG are supplementary -- Linear pair postulate; 4. ∠CQH ≅ ∠GQD -- ?.

  2. Ari proves the vertical angles theorem on open scissors, blades along CG and DH. Which reason fills the blank?

    • Linear pair postulate
    • Vertical angles theorem
    • Congruent complements theorem
    • Congruent supplements theorem

  3. Kira proves the alternate exterior angles theorem on train rails UV and WY, crossed by road HD. Which reason fills the blank?

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

  4. Use this

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

  5. Luz proves the alternate exterior angles theorem on map streets UV and WY, crossed by avenue HD. Which reason fills the blank?

    • Vertical angles theorem
    • Same-side interior angles theorem
    • Converse of the corresponding angles postulate
    • Corresponding angles postulate

  6. Use this

    Given: m∠CQH = 115. Prove: m∠HQG = 65. Ladder: 1. m∠CQH = 115 -- Given; 2. ∠CQH and ∠HQG are supplementary -- Linear pair postulate; 3. m∠CQH + m∠HQG = 180 -- Definition of supplementary angles; 4. 115 + m∠HQG = 180 -- Substitution property; 5. m∠HQG = 65 -- ?.

  7. Pia opens scissors so one angle at the pivot Q measures 115°. Which reason fills the blank?

    • Given
    • Addition property of equality
    • Subtraction property of equality
    • Substitution property

  8. Use this

    Sketch, not to scale: lines CG and DH cross at Q (C upper left, H upper right, G lower right, D lower left). Marked: ∠GQD labeled 128°. Given: m∠GQD = 128. Prove: m∠DQC = 52. Ladder: 1. m∠GQD = 128 -- Given; 2. ∠GQD and ∠DQC are supplementary -- Linear pair postulate; 3. m∠GQD + m∠DQC = 180 -- Definition of supplementary angles; 4. 128 + m∠DQC = 180 -- Substitution property; 5. m∠DQC = 52 -- ?.

  9. Ren sets kite sticks CG and DH so one angle at Q measures 128°. Which reason fills the blank?

    • Addition property of equality
    • Definition of supplementary angles
    • Subtraction property of equality
    • Given

  10. Use this

    Marked: none beyond the lines. Given: lines CG and DH cross at Q. Prove: ∠HQG ≅ ∠DQC. Ladder: 1. Lines CG and DH cross at Q -- Given; 2. ∠HQG and ∠CQH are supplementary -- Linear pair postulate; 3. ? -- Linear pair postulate; 4. ∠HQG ≅ ∠DQC -- Congruent supplements theorem.

  11. Jun proves the vertical angles theorem with scissors opened wide. Which statement fills the blank?

    • ∠HQG ≅ ∠DQC
    • ∠DQC and ∠CQH are complementary
    • ∠DQC and ∠CQH are supplementary
    • ∠DQC ≅ ∠CQH

  12. Use this

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

  13. Milo proves the alternate interior angles theorem on rug stripes UV and WY, crossed by seam HD. Which statement fills the blank?

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

  14. Use this

    Given: UV ∥ WY. Prove: ∠VSQ ≅ ∠SQW. Ladder: 1. UV ∥ WY -- Given; 2. ∠VSQ ≅ ∠YQD -- Corresponding angles postulate; 3. ? -- Vertical angles theorem; 4. ∠VSQ ≅ ∠SQW -- Transitive property.

  15. Noah proves the alternate interior angles theorem on window bars UV and WY, crossed by brace HD. Which statement fills the blank?

    • ∠VSQ ≅ ∠SQW
    • ∠YQD ≅ ∠SQY
    • ∠YQD ≅ ∠SQW
    • ∠VSQ ≅ ∠SQY

  16. Use this

    Given: UV ∥ WY and m∠HSV = 62. Prove: m∠SQY = 62. Ladder: 1. UV ∥ WY -- Given; 2. m∠HSV = 62 -- Given; 3. ? -- Corresponding angles postulate; 4. m∠SQY = m∠HSV -- Definition of congruent angles; 5. m∠SQY = 62 -- Substitution property.

  17. Tala measures 62° where road HD meets train rail UV. Which statement fills the blank?

    • ∠HSV ≅ ∠YQD
    • UV ∥ WY
    • m∠SQY = 62
    • ∠HSV ≅ ∠SQY

  18. Use this

    Given: UV ∥ WY and m∠USQ = 74. Prove: m∠SQY = 74. Ladder: 1. UV ∥ WY -- Given; 2. m∠USQ = 74 -- Given; 3. ? -- Alternate interior angles theorem; 4. m∠SQY = m∠USQ -- Definition of congruent angles; 5. m∠SQY = 74 -- Substitution property.

  19. Zee measures 74° where pole HD meets bar UV of a bike rack. Which statement fills the blank?

    • ∠USQ ≅ ∠SQY
    • UV ∥ WY
    • ∠USQ ≅ ∠SQW
    • m∠SQY = 74
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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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