# 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.

**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 .

**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 .

- A 116 cm,
- B 58 cm,
- C 116 cm,
- D 58 cm,
- E 116 cm,

**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.
- DWe cannot conclude anything, because we need more information.

**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