Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Start Practicing

Worksheet: Perpendicular Bisector Theorem and Its Converse

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:

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

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 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 measure
  • Ewhen it connects two angles

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