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.
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
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 .
Given that , , and , find the value of .