# 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 ? Q3:

The given figure shows an isosceles triangle, where is the midpoint of . Can we prove that triangle and triangle 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 and ?

• AThe angle is bigger than the angle , because the two triangles are congruent.
• BThe angle is bigger than the angle , because the two triangles are congruent.
• CThe angles have the same measure, because the triangles are congruent.

Q4:

In , if and , find .

Q5:

Given that , , and , find the value of . • A18
• B4
• C13
• D12
• E26

Q6:

Find . 