Points on a perpendicular bisector or on an angle bisector

Answer Key - Grade 10 Math Worksheet - Building Confidence

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

1. 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?

   13
2. 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?

   17
3. 3.

   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?

   9
4. 4.

   Pia sets a lamp Q on the bisector of a wall corner, ∠CVW. Q is 6 ft from side VC, and QV = 10 ft. How far is Q from side VW, in ft?

   6
5. 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?

   5
6. 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?

   8
7. 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?

   9
8. 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 lies on the perpendicular bisector of DF.
   • Q is the midpoint of DF.
   • Q lies on the bisector of ∠CVW.
   • Q lies on segment DF.
9. 9.

   Bo draws segment GH and ∠UVY in crayon. Q is inside ∠UVY, 4 inches from each side. Which must be true?

   • Q lies on the bisector of ∠UVY.
   • Q lies on the perpendicular bisector of GH.
   • Q lies on side VU.
   • Q is the corner V.
10. 10.

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