PencilGo

Grade 10 · Math · Geometry

10th grade Which angle pairs prove that two lines are parallel? worksheet

6 printable versionsOn Level10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

When it’s done, scan the sheet with your phone and PencilGo marks it and picks the next one. Create a free account

Version
Print

Which angle pairs prove that two lines are parallel?

Grade 10 Math Worksheet

NameDate

Circle the best answer, or write your answer on the line.

  1. Read this first

    Sketch, not to scale

    Lines DF and QS (no arrows given), crossed by line UV at G on DF and at H on QS; U is above, V below; D and Q are on the left. Proof. Step 1: Given m∠DGH = 64° and m∠SHV = 116°. Step 2: m∠GHQ = 116°, because ∠SHV and ∠GHQ are vertical angles, so they are congruent. Step 3: m∠DGH + m∠GHQ = 180°, so DF ∥ QS. Reason for Step 3: ?

  2. Kira is writing a two-column proof that DF ∥ QS. Which reason justifies Step 3?

    • Vertical angles are congruent (the reason for Step 2)
    • If corresponding angles are congruent, then the lines are parallel (converse of the Corresponding Angles Theorem)
    • If lines are parallel, then same-side interior angles are supplementary (Same-Side Interior Angles Theorem)
    • If same-side interior angles are supplementary, then the lines are parallel (converse of the Same-Side Interior Angles Theorem)

  3. Use this

    Proof. Step 1: Given m∠UGF = 125° and m∠GHQ = 55°. Step 2: m∠FGH = 55°, because ∠UGF and ∠FGH are a linear pair, so they add to 180°. Step 3: m∠FGH = m∠GHQ, so DF ∥ QS. Reason for Step 3: ?

  4. Luz is writing a two-column proof that DF ∥ QS. Which reason justifies Step 3?

    • If lines are parallel, then alternate interior angles are congruent (Alternate Interior Angles Theorem)
    • If alternate interior angles are congruent, then the lines are parallel (converse of the Alternate Interior Angles Theorem)
    • If same-side interior angles are supplementary, then the lines are parallel (converse of the Same-Side Interior Angles Theorem)
    • Linear pair angles add to 180° (the reason for Step 2)

  5. Sketch, not to scale

    Lines DF and QS (no arrows given), crossed by line UV at G on DF and at H on QS; U is above, V below; D and Q are on the left. Proof. Step 1: Given m∠UGF = 100° and m∠SHV = 80°. Step 2: m∠UGD = 80°, because ∠UGF and ∠UGD are a linear pair, so they add to 180°. Step 3: m∠UGD = m∠SHV, so DF ∥ QS. Reason for Step 3: ?

  6. Milo is writing a two-column proof that DF ∥ QS. Which reason justifies Step 3?

    • If alternate interior angles are congruent, then the lines are parallel (converse of the Alternate Interior Angles Theorem)
    • If alternate exterior angles are congruent, then the lines are parallel (converse of the Alternate Exterior Angles Theorem)
    • Linear pair angles add to 180° (the reason for Step 2)
    • If lines are parallel, then alternate exterior angles are congruent (Alternate Exterior Angles Theorem)

  7. Noah is proving DF ∥ QS from an equation. Step 3 is missing. Which statement belongs there?

    • x = 14, from the given
    • ∠UGF and ∠GHS are alternate interior angles, and they are congruent
    • ∠UGF and the angle next to it on line UV are a linear pair
    • ∠UGF and ∠GHS are corresponding angles, and they are congruent

  8. Pia is proving DF ∥ QS from an equation. Step 3 is missing. Which statement belongs there?

    • ∠DGH and the angle next to it on line UV are a linear pair
    • x = 19, from the given
    • ∠DGH and ∠GHS are alternate interior angles, and they are congruent
    • ∠DGH and ∠GHS are corresponding angles, and they are congruent

  9. Ren is proving DF ∥ QS from an equation. Step 3 is missing. Which statement belongs there?

    • x = 20, from the given
    • ∠UGD and ∠SHV are same-side exterior angles, and they are congruent
    • ∠UGD and ∠SHV are alternate exterior angles, and they are congruent
    • ∠UGD and the angle next to it on line DF are a linear pair

  10. Tala is proving DF ∥ QS from an equation. Step 3 is missing. Which statement belongs there?

    • ∠DGH and the angle next to it on line UV are a linear pair
    • x = 13, from the given
    • ∠DGH and ∠QHV are corresponding angles, and they are congruent
    • ∠DGH and ∠QHV are alternate interior angles, and they are congruent

  12. Esme checks two guitar strings. ∠DGH and ∠GHS are alternate interior angles, m∠DGH = (4x + 2)° and m∠GHS = (2x + 40)°. What value of x makes DF ∥ QS?

  13. Jun checks two streets on a map. ∠UGD and ∠SHV are alternate exterior angles, m∠UGD = (6x − 15)° and m∠SHV = (4x + 25)°. What value of x makes DF ∥ QS?

    Use the picture in question 8.

  14. Kira checks the two rails of a ladder. ∠DGH and ∠QHV are corresponding angles, m∠DGH = (5x − 6)° and m∠QHV = (3x + 20)°. What value of x makes DF ∥ QS?

    Use the picture in question 8.

PencilGopencilgo.com

10th grade Which angle pairs prove that two lines are parallel? worksheet – printable
Print: 123456

About this worksheet

Proving lines parallel. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can decide from two angle measures whether two lines are parallel, and say which rule decides it.
  • I can choose a fact, and the converse that goes with it, that proves two lines parallel.
  • I can find the value of x that makes two lines parallel, give the reason for a step in a proof, name a missing step, and find an angle across two pairs of parallel sides.

Standard: G-CO.C.9 (converses; related, the CCSS text names the forward theorems)

Words to know

converse: The if-then rule turned around: "if the angles are equal, then the lines are parallel".

prove parallel: Show from angles that two lines never meet.

one crossing: The angles around G only (or H only); facts there hold for any lines.

not to scale: The sketch's look does not count; only the numbers do.

Common mistakes

Your child expected equal pairs (corresponding or alternate angles) to add to 180°.

Your child expected same-side angles to be equal; for parallel lines they add to 180°.

Your child decided from how the sketch looks.

What to say

Ask: for parallel lines, which pairs match in size?

Ask: is one angle wide and the other narrow?

Ask: does the sketch say it is drawn to scale?

Questions parents ask

What is the most common mistake with which angle pairs prove that two lines are parallel??

Your child expected equal pairs (corresponding or alternate angles) to add to 180°.

How can I help my child with which angle pairs prove that two lines are parallel??

Ask: for parallel lines, which pairs match in size?

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

See all Geometry

Every sheet you scan goes into your child’s record: dated, marked and ready for the year-end portfolio. Homeschool records

Ready for easier practice?

Print a sheet, scan it when it’s done, and PencilGo picks the next one.

Create a free account