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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 - Challenge Me

NameDate

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

  1. Kira hangs a lamp Q in a room corner. Q is 6 ft from each side of ∠CVW. m∠CVQ = (3x + 4)° and m∠QVW = (5x − 12)°. What is m∠CVW?

  2. Luz plants a tree S where two paths meet. S is 9 m from each side of ∠DGF. m∠DGS = (2x + 11)° and m∠SGF = (4x − 9)°. What is m∠DGF?

  3. Milo marks a lookout Q between two roads. Q is 4 km from each side of ∠UHY. m∠UHQ = (6x − 5)° and m∠QHY = (4x + 9)°. What is m∠UHY?

  4. Ren folds a paper sheet. H is on the perpendicular bisector of CW. HC = 4x − 2, HW = 2x + 12 and CS = x + 3, in inches. How long is CW?

  5. Tala maps a park fountain. Q is on the perpendicular bisector of UY. QU = 6x + 5, QY = 3x + 26 and UV = 4x + 2, in m. How long is UY?

  6. Zee sets up a tent. C is on the perpendicular bisector of SD. CS = 2x + 13, CD = 5x − 11 and SW = 3x − 3, in ft. How long is SD?

  7. Ari plots two towns D and F on a map grid and checks a spot Q: D(0, 2), F(6, 4) and Q(3, 7). Is Q on the perpendicular bisector of DF?

    • No: QD² = 34 but QF² = 18, so QD ≠ QF.
    • Yes: Q is higher than both D and F.
    • Yes: Q is straight above the midpoint (3, 3) of DF.
    • Yes: Q is 3 squares across from D and 3 squares across from F.

  8. Bo plots two park gates G and W on a grid and checks a spot S for a bench: G(2, 1), W(0, 5) and S(5, 5). Is S on the perpendicular bisector of GW?

    • No: SG is 7 squares and SW is 5 squares.
    • No: S is not straight above the midpoint (1, 3) of GW.
    • Yes: SG² = 25 and SW² = 25, so SG = SW = 5.
    • No: S is not on segment GW.

  9. Esme plots two classroom doors C and U on a grid and checks a spot H for a sign: C(3, 1), U(7, 3) and H(4, 6). Is H on the perpendicular bisector of CU?

    • Yes: H is higher than both C and U.
    • No: HC² = 26 but HU² = 18, so HC ≠ HU.
    • Yes: HC and HU are both 6 squares.
    • Yes: H is 3 squares above U and 3 squares across from U.

  10. Jun plots two trees Y and V on a grid and checks a spot D for a lamp: Y(2, 3), V(6, 1) and D(6, 6). Is D on the perpendicular bisector of YV?

    • No: D is not straight above the midpoint (4, 2) of YV.
    • Yes: DY² = 25 and DV² = 25, so DY = DV = 5.
    • No: D is not on segment YV.
    • No: DY is 7 squares and DV is 5 squares.
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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

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