Bisectors in Triangles - Perpendicular Bisector Theorem & Examples

The properties of perpendicular bisectors in triangles, including the Perpendicular Bisector Theorem, its converse, and practical examples to enhance your understanding. Discover how angle bisectors relate to isosceles triangles and their vertex angles.

• Triangles
• Bisectors
• Theorem
• Examples
• Isosceles

rsyi Follow

Uploaded on Apr 19, 2025 | 0 Views

Download Presentation

Please find below an Image/Link to download the presentation.

The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author.If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.

You are allowed to download the files provided on this website for personal or commercial use, subject to the condition that they are used lawfully. All files are the property of their respective owners.

The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author.

Presentation Transcript

1. Unit 5 Unit 5- -3 3 Bisectors in Triangles Bisectors in Triangles PLANE GEOMETRY PLANE GEOMETRY

2. Perpendicular Bisector ?? ?? ??? ????????????? ???????? ?? ??

3. Perpendicular Bisector Theorem: If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

4. Converse of the Perpendicular Bisector Theorem: If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.

5. Example 1: ?? is the perpendicular bisector of ??. Find CA and DB. ? ? ? ? ? ? ?

6. Example 2: ?? is the perpendicular bisector of ??. Find x, CA, and CB. ? ? ? ?

7. Angle Bisector Theorem: If a point is on the bisector of an angle, then the point is equidistant from the sides of the angle. Converse of the Angle Bisector Theorem: If a point in the interior of an angle is equidistant from the sides of the angle, then the point is on the angle bisector.

8. Example 3: ?? is the Angle Bisector. Find x, CA, and CB. ? ?? ? ? ? ?? + ? ?

9. Isosceles Triangles and Angle Bisectors Isosceles Triangles and Angle Bisectors The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base. ? ? ? ?

10. Example 4: ?? is the Angle Bisector. Find x and y. M y x 63 L N O

11. Example 5: Is C on the Angle Bisector? ? ? ? ? ? ? ? ? ? ? ? ?