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

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Points on a perpendicular bisector or on an angle bisector

Grade 10 Math Worksheet

NameDate

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

  1. Kira draws the perpendicular bisector of kite crossbar DF. Q is on it, QD = 3x + 5 and QF = 5x − 13, in cm. How long is QD?

  2. Luz folds paper along the perpendicular bisector of edge SU. H is on it, HS = 2x + 15 and HU = 5x − 6, in inches. How long is HS?

  3. Milo walks the perpendicular bisector of park path CY. Q is on it, QC = 5x − 6 and QY = 2x + 18, in m. How long is QC?

  4. Noah pegs a rope on the perpendicular bisector of tent edge WD. S is on it, SW = x + 21 and SD = 4x − 9, in ft. How long is SW?

  5. Pia hangs a lamp in a corner. Q is on ray VS, the bisector of ∠CVW. Its distances to the sides are 3x + 1 and x + 13, in ft. What is x?

  6. Zee places a vase on a rug corner. D is on ray WC, the bisector of ∠GWS. Its distances to the sides are 2x + 9 and 6x − 11, in inches. What is x?

  7. Ari checks a point Q drawn above a kite's crossbar DF, whose midpoint is G. QD = 9 cm and QF = 9 cm. Is Q on the perpendicular bisector of DF?

    • No: Q is not on segment DF.
    • No: 9 cm is not half of DF.
    • Yes: Q is the same distance from D and from F.
    • We cannot tell: no right angle is marked at G.

  8. Bo checks where a bench H stands near a straight park path CW, whose midpoint is S. HC = 11 m and HW = 13 m. Is H on the perpendicular bisector of CW?

    • Yes: in the sketch, H looks as if it is straight above S.
    • Yes: 11 m and 13 m are close enough to count as equal.
    • No: H is 11 m from C but 13 m from W.
    • We cannot tell: no right angle is marked at S.

  9. Esme checks a lamp hook Q inside the shelf corner ∠DVF. QU = QY = 7 inches, with no right angle marked at the sides. Is Q on the bisector of the angle?

    • No: 7 inches is too far from the corner V.
    • We cannot tell: QU and QY are not marked at right angles to the sides.
    • Yes: in the sketch, Q looks halfway between the two sides.
    • Yes: Q is 7 inches from both sides.

  10. Jun checks a tent stake S inside ∠CGW. SH = SD = 5 ft, with no right angle marked at the sides. Is S on the bisector of the angle?

    • Yes: in the sketch, S looks as if it sits on the middle line.
    • Yes: SH = SD, so S is the same distance from both sides.
    • We cannot tell: SH and SD are not marked at right angles to the sides.
    • No: S is not on either side of the corner.
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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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