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Grade 10 · Math · Geometry

10th grade Midpoints and bisectors of segments and angles worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

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Midpoints and bisectors of segments and angles

Grade 10 Math Worksheet - Building Confidence

NameDate

Circle the best answer.

  1. On Ari's number line, A is at −7 and B is at 11. M is the midpoint of AB. What number is at M?

    • 4
    • −2
    • 9
    • 2

  2. M is the midpoint of AB, for Esme's kite. AM = (3x + 2) m and MB = (5x − 8) m. What is AM?

    • 5 m
    • 17 m
    • 8.5 m
    • 34 m

  3. Ray BD bisects ∠ABC on Jun's protractor. m∠ABD = (4x + 6)° and m∠DBC = (6x − 10)°. What is m∠ABC?

    • 152°
    • 8°
    • 76°
    • 38°

  4. Ray BD bisects ∠ABC in Kira's drawing. m∠ABC = (8x + 4)° and m∠DBC = (5x − 4)°. What is m∠DBC?

    • 26°
    • 13°
    • 52°
    • 6°

  5. Ray BD bisects ∠ABC in Luz's drawing. m∠ABD = (3x + 11)° and m∠DBC = (7x − 29)°. What is m∠ABD?

    • 10°
    • 41°
    • 20.5°
    • 82°

  6. Ray BD bisects ∠ABC in Noah's drawing. Which statement must be true?

    • BD ⊥ BA
    • m∠ABD = m∠ABC
    • m∠ABD = m∠DBC
    • m∠ABC = ½ m∠ABD

  7. Line ℓ is the perpendicular bisector of AB, and it meets AB at M. Which statement must be true for Pia's diagram?

    • AM = AB, and ℓ is perpendicular to AB.
    • AM = MB, but ℓ may meet AB at any angle.
    • AB = ½ AM, and ℓ is perpendicular to AB.
    • AM = MB, and ℓ meets AB at a right angle.

  8. M is the midpoint of AB and N is the midpoint of AM in Ren's drawing. AB = 24 cm. What is AN?

    • 6 cm
    • 3 cm
    • 12 cm
    • 18 cm

  9. P is the midpoint of AB and Q is the midpoint of PB. AB = 20 cm. What is AQ, for Tala's drawing?

    • 15 cm
    • 7.5 cm
    • 5 cm
    • 10 cm

  10. M is the midpoint of AB and N is the midpoint of MB in Zee's drawing. MN = 7 cm. What is AB?

    • 21 cm
    • 28 cm
    • 14 cm
    • 56 cm
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10th grade Midpoints and bisectors of segments and angles worksheet – printable
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About this worksheet

Midpoints and bisectors. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can use a midpoint or a bisector to set up an equation (linear or quadratic), reject a root that makes a length or angle negative, and find the length or angle asked for.
  • I can chain midpoints and bisectors, and use bisectors of adjacent and vertical angles.
  • I can pick the reason that justifies a step, give a counterexample to a converse, and use a perpendicular bisector in a fold, a bus-stop and a chord problem.

Standard: G-CO.A.1

Words to know

midpoint: The point that cuts a segment into two equal halves.

bisect: Cut into two equal parts.

angle bisector: A ray from the corner that cuts an angle into two equal angles.

m∠DFG: The measure of angle DFG in degrees; F, the middle letter, is the corner.

tick marks, arcs: Marks on a sketch: the same mark means the same length or angle.

Common mistakes

Your child gave one half where the whole, or a different piece, was asked. Re-read which piece the question names.

Your child added the endpoints but did not divide by 2, or added the wrong two numbers. A midpoint is the average of the ends.

Your child put the answer on the wrong side of a point. Check which way along the line the answer lies.

Questions parents ask

What is the most common mistake with midpoints and bisectors of segments and angles?

Your child gave one half where the whole, or a different piece, was asked. Re-read which piece the question names.

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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