Worksheet: Perpendicular Bisector Theorem and Its Converse

In this worksheet, we will practice using the perpendicular bisector and its theorem, the converse of the perpendicular bisector theorem, and the circumcenter theorem.

Q1:

For which values of π‘₯ and 𝑦 is 𝐴 𝐷 a perpendicular bisector of 𝐡 𝐢 ?

  • A π‘₯ = 4 3 , 𝑦 = 3 5
  • B π‘₯ = 2 3 , 𝑦 = 1
  • C π‘₯ = 8 3 , 𝑦 = 7 5
  • D π‘₯ = 2 , 𝑦 = 1
  • E π‘₯ = 2 , 𝑦 = 7 5

Q2:

Determine whether 𝐴 𝐸 is a perpendicular bisector of 𝐡 𝐢 .

  • AIt is not a perpendicular bisector.
  • BIt is a perpendicular bisector.

Q3:

In the diagram, 𝐴 𝐡 = 6 and 𝐡 𝐷 = 5 .

Find 𝐴 𝐢 .

Find 𝐢 𝐷 .

Q4:

In the diagram, 𝐴 𝐷 is the perpendicular bisector of 𝐡 𝐢 . Find the value of π‘₯ .

Q5:

What makes an intersecting line a perpendicular bisector?

  • Awhen the two lines meet at a right angle and the segment of each line is consequently of equal length
  • Bwhen the intersecting line divides the other into two line segments of equal length
  • Cwhen the line intersects a line segment at an acute angle and divides it into two line segments of equal length
  • Dwhen the line intersects a line segment at right angles and divides it into two line segments of equal length
  • Ewhen the line intersects a line segment at an obtuse angle and divides it into two line segments of equal length

Q6:

When is a line said to be an angle bisector?

  • Awhen it cuts another line segment into two equal parts
  • Bwhen it divides an angle into two distinct angles
  • Cwhen it cuts another line segment into two distinct parts
  • Dwhen it divides an angle into two angles of equal size
  • Ewhen it connects two angles

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