# Worksheet: Perpendicular Bisector Theorem and Its Converse

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:

For which values of and is a perpendicular bisector of ? • A,
• B,
• C,
• D,
• E,

Q2:

Determine whether is a perpendicular bisector of . • AIt is a perpendicular bisector.
• BIt is not a perpendicular bisector.

Q3:

In the diagram, and . Find .

Find .

Q4:

In the diagram, is the perpendicular bisector of . Find the value of . Q5:

What makes an intersecting line a perpendicular bisector?

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

Q6:

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

Q7:

In the following figure, find the length of . Q8:

In the following figure, find the length of . Q9:

In the figure, what is the length of ? Q10:

Find the length of and . • A116 cm,
• B58 cm,
• C116 cm,
• D58 cm,
• E116 cm,

Q11:

What is ? Q12:

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.

Q13:

Find . Q14:

In , if and , find .

Q15:

In the figure below, what is the area of ? Q16:

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

Q17:

Find . 