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.

Q1:

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

Q2:

What is π‘šβˆ π‘‹πΆπ΅?

Q3:

The given figure shows an isosceles triangle, where 𝑀 is the midpoint of 𝐴𝐡.

Can we prove that triangle 𝐴𝐢𝑀 and triangle 𝐡𝐢𝑀 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 𝐢𝐴𝐡 and 𝐴𝐡𝐢?

  • AThe angle 𝐢𝐴𝐡 is bigger than the angle 𝐴𝐡𝐢, because the two triangles are congruent.
  • BThe angle 𝐴𝐡𝐢 is bigger than the angle 𝐢𝐴𝐡, 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.

Q4:

In △𝐴𝐡𝐢, if 𝐴𝐡=𝐴𝐢 and π‘šβˆ π΄=52∘, find π‘šβˆ π΅.

Q5:

Given that 𝐢𝐴=𝐢𝐷=𝐴𝐡, π‘šβˆ π·πΆπ΄=48∘, and π‘šβˆ π΄π΅πΆ=(3π‘₯+21)∘, find the value of π‘₯.

  • A18
  • B4
  • C13
  • D12
  • E26

Q6:

Find π‘₯.

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