Lesson Worksheet: Perpendicular Bisector Theorem and Its Converse Mathematics • 11th Grade

In this worksheet, we will practice using the perpendicular bisector theorem and its converse to find a missing angle or side in an isosceles triangle.


When is a line said to be an angle bisector?

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


What is ๐‘šโˆ ๐‘‹๐ถ๐ต?


The given figure shows an isosceles triangle, where ๐‘€ is the midpoint of ๐ด๐ต.

Can we prove that triangle ๐ด๐ถ๐‘€ and triangle ๐ต๐ถ๐‘€ are congruent? If yes, state which congruence criteria could be used.

  • AYes, SAS
  • BNo
  • CYes, ASA
  • DYes, SSS

Hence, what can we conclude about the angles ๐ถ๐ด๐ต and ๐ด๐ต๐ถ?

  • AThe angle ๐ถ๐ด๐ต is bigger than the angle ๐ด๐ต๐ถ, because the two triangles are congruent.
  • BThe angle ๐ด๐ต๐ถ is bigger than the angle ๐ถ๐ด๐ต, because the two triangles are congruent.
  • CThe angles have the same measure, because the triangles are congruent.
  • DWe cannot conclude anything, because we need more information.


In โ–ณ๐ด๐ต๐ถ, if ๐ด๐ต=๐ด๐ถ and ๐‘šโˆ ๐ด=52โˆ˜, find ๐‘šโˆ ๐ต.


Given that ๐ถ๐ด=๐ถ๐ท=๐ด๐ต, ๐‘šโˆ ๐ท๐ถ๐ด=48โˆ˜, and ๐‘šโˆ ๐ด๐ต๐ถ=(3๐‘ฅ+21)โˆ˜, find the value of ๐‘ฅ.

  • A18
  • B4
  • C13
  • D12
  • E26


Find ๐‘ฅ.

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