Grade 10 · Math · Geometry

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

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

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Which angle pairs prove that two lines are parallel?

Grade 10 Math Worksheet - Building Confidence

NameDate

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

1.
Milo checks the two rails of a ladder. ∠DGH and ∠GHQ are same-side interior angles, m∠DGH = 68° and m∠GHQ = 112°. Is line DF parallel to line QS?
- No: same-side interior angles must be equal.
- Yes: the angles add to 180°.
- No: 112° is an obtuse angle.
2.
Noah checks two window bars. ∠FGH and ∠GHQ are alternate interior angles, m∠FGH = 64° and m∠GHQ = 66°. Is line DF parallel to line QS?
Use the picture in question 1.
- No: alternate interior angles must add to 180°.
- No: 64° and 66° are not equal.
- Yes: the lines look parallel in the sketch.
3.
Ren draws two lines on paper. Which fact proves that line DF ∥ line QS?
Use the picture in question 1.
- m∠UGD = m∠FGH
- m∠DGH = m∠GHQ
- m∠UGF = m∠GHS
- m∠UGF + m∠FGH = 180°
4.
Tala checks two bike lanes. Which fact proves that line DF ∥ line QS?
Use the picture in question 1.
- m∠FGH = m∠GHS
- m∠DGH = m∠GHS
- m∠GHQ + m∠QHV = 180°
- m∠QHV = m∠GHS
5.
Zee checks two stripes on a rug. Which fact proves that line DF ∥ line QS?
Use the picture in question 1.
- m∠FGH + m∠UGF = 180°
- m∠UGD = m∠UGF
- m∠FGH + m∠GHS = 180°
- m∠FGH + m∠GHQ = 180°
6.
Ari draws two lines in crayon. Which fact proves that line DF ∥ line QS?
Use the picture in question 1.
- m∠UGD = m∠SHV
- m∠UGD = m∠FGH
- m∠SHV = m∠QHV
- m∠UGD + m∠SHV = 180°
Bo checks two guitar strings. ∠DGH and ∠GHQ are same-side interior angles, and m∠DGH = 81°. What must m∠GHQ be for DF ∥ QS, in degrees?
Use the picture in question 1.
Esme draws two lines on paper. ∠FGH and ∠GHS are same-side interior angles, and m∠FGH = 116°. What must m∠GHS be for DF ∥ QS, in degrees?
Use the picture in question 1.
Jun checks two bike lanes. ∠UGD and ∠QHV are same-side exterior angles, and m∠UGD = 72°. What must m∠QHV be for DF ∥ QS, in degrees?
Use the picture in question 1.
Kira checks two window bars. ∠UGF and ∠SHV are same-side exterior angles, and m∠UGF = 127°. What must m∠SHV be for DF ∥ QS, in degrees?
Use the picture in question 1.

10th grade Which angle pairs prove that two lines are parallel? worksheet – printable — Print: 1 2 3 4 5 6

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

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