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Lesson: Perpendicular Bisector Theorem and Its Converse

Sample Question Videos

Worksheet • 6 Questions • 1 Video

Q1:

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

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

Q2:

What makes an intersecting line a perpendicular bisector?

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

Q3:

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

Q4:

When is a line said to be an angle bisector?

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

Q5:

In the diagram, 𝐴 𝐡 = 6 and 𝐡 𝐷 = 5 .

Find 𝐴 𝐢 .

Find 𝐢 𝐷 .

Q6:

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

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