1 / 15

Properties of Perpendicular Bisector & Circumcenter Properties of Angle Bisectors & Incenter

Properties of Perpendicular Bisector & Circumcenter Properties of Angle Bisectors & Incenter. Notes 29 – Section 5.1. Essential Learnings. Students will understand and be able to identify and use perpendicular bisectors in triangles.

lani
Download Presentation

Properties of Perpendicular Bisector & Circumcenter Properties of Angle Bisectors & Incenter

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Properties of Perpendicular Bisector & CircumcenterProperties of Angle Bisectors & Incenter Notes 29 – Section 5.1

  2. Essential Learnings • Students will understand and be able to identify and use perpendicular bisectors in triangles. • Students will understand and be able to identify and use angle bisectors in triangles.

  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. B 5 5 A C 4 D 4

  4. Example 1 Find the measure of PQ. Q 3x+1 5x-3 P R S

  5. Vocabulary Concurrent lines – when three or more lines intersect at a common point called the point of concurrency. Point of concurrency

  6. Circumcenter The perpendicular bisectors of a triangle intersect at a point called the circumcenter that is equidistant from the vertices of the triangle.

  7. Construct Circumcenter 1. Draw a triangle 2. Construct perpendicular bisectors of each side of the triangle. 3. Intersection of three bisectors is the circumcenter.

  8. Angle Bisector Theorem If a point is on the bisector of an angle, then it is equidistant from the sides of the angle. C D B A

  9. Example 2 Find the measure of AD. A D 5 B C

  10. Example 3 Find the measure of ∠WYZ. X W 28° Y Z

  11. Example 4 Find the measure of QS. Q S P R

  12. Incenter The angle bisectors of a triangle intersect at a point called the incenter that is equidistant from each side of the triangle.

  13. Construct Incenter 1. Draw a triangle 2. Construct the three angle bisectors of the triangle. 3. Intersection of three angle bisectors is the incenter. The incenter is equidistant from each side.

  14. Constructions • Equilateral Triangle • Regular Hexagon • Square

  15. Assignment Page 327: 1-3, 9-14, 21-24, 32-34 Constructions Worksheet Unit Study Guide 8

More Related