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.
Determine whether is a perpendicular bisector of .
- AIt is a perpendicular bisector.
- BIt is not a perpendicular bisector.
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
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
In the following figure, find the length of .
In the figure, what is the length of ?
Find the length of and .
- A116 cm,
- B58 cm,
- C116 cm,
- D58 cm,
- E116 cm,
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
- 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.
In , if and , find .
In the figure below, what is the area of ?
Given that , , and , find the value of .