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10th grade Points on a perpendicular bisector or on an angle bisector worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

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Points on a perpendicular bisector or on an angle bisector

Grade 10 Math Worksheet - Building Confidence

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

  1. Kira builds a kite whose spine, through Q, is the perpendicular bisector of crossbar DF. QD = 13 cm and DF = 10 cm. How long is QF, in cm?

  2. Luz pitches a tent whose pole SH is the perpendicular bisector of edge CW. HC = 17 inches and CW = 16 inches. How long is HW, in inches?

  3. Milo plants a tree at Q, on the perpendicular bisector of park path UY. QU = 26 m and UY = 20 m. How long is QY, in m?

  4. Noah hangs a swing at W, on the perpendicular bisector of the bar FC. WF = 9 ft and FC = 14 ft. How long is WC, in ft?

  5. Ren plants a tree Q on the bisector of a path corner, ∠DGF. Q is 5 m from side GD, and QG = 13 m. How far is Q from side GF, in m?

  6. Tala marks a camp S on the bisector of a road angle, ∠UHY. S is 8 km from side HU, and SH = 17 km. How far is S from side HY, in km?

  7. Zee stands at a tower D on the bisector of a fence corner, ∠GWS. D is 9 m from side WG, and DW = 15 m. How far is D from side WS, in m?

  8. Ari draws segment DF and ∠CVW on paper. Q is 7 cm from D and 7 cm from F. Which must be true?

    • Q is the midpoint of DF.
    • Q lies on segment DF.
    • Q lies on the perpendicular bisector of DF.
    • Q lies on the bisector of ∠CVW.

  9. Esme studies a map with road UW and field corner ∠DGF. S is 12 m from U and 12 m from W. Which must be true?

    • S is the midpoint of UW.
    • S lies on the bisector of ∠DGF.
    • S lies on the perpendicular bisector of UW.
    • S lies on segment UW.

  10. Jun looks at a rug with seam CY and corner ∠QHS. D is inside ∠QHS, 3 ft from each side. Which must be true?

    • D is the corner H.
    • D lies on side HQ.
    • D lies on the perpendicular bisector of CY.
    • D lies on the bisector of ∠QHS.
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10th grade Points on a perpendicular bisector or on an angle bisector worksheet – printable
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About this worksheet

Points on a perpendicular bisector or on an angle bisector. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can use a perpendicular bisector to find a distance from a point to the end of a segment, and an angle bisector to find a distance to a side.
  • I can tell which bisector a point lies on from its distances, and say when the marks are not enough to tell.
  • I can set two equal distances equal, solve for x, and give the length, x or angle asked for, also on a grid.

Standard: G-CO.C.9 (perpendicular bisector); the angle-bisector version is not in the CCSS text

Words to know

perpendicular bisector: A line through a segment's midpoint at a right angle to it.

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

equidistant: The same distance from two things.

distance to a side: The length of the segment that meets the side at a right angle.

⊥: Is perpendicular to: meets at a right angle.

Common mistakes

Your child gave the length of the segment instead of the distance from the point to its other end.

Your child gave half the segment, the distance from the end to the midpoint, not to the point.

Your child used the slanted length from the point to the corner, not the distance to the side.

What to say

Ask: which two points does the question name?

Ask: does the segment you found end at the point?

Ask: is that segment at a right angle to the side?

Questions parents ask

What is the most common mistake with points on a perpendicular bisector or on an angle bisector?

Your child gave the length of the segment instead of the distance from the point to its other end.

How can I help my child with points on a perpendicular bisector or on an angle bisector?

Ask: which two points does the question name?

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

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