1 / 15

5.2 Bisectors of a Triangle

5.2 Bisectors of a Triangle. Goal : To use segment bisectors and perpendicular lines to solve problems involving triangles and real world scenarios. A perpendicular bisector of a triangle is a line (or ray or segment) that is perpendicular to a side of the triangle at the midpoint of the side.

cachez
Download Presentation

5.2 Bisectors of a Triangle

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. 5.2 Bisectors of aTriangle Goal: To use segment bisectors and perpendicular lines to solve problems involving triangles and real world scenarios.

  2. A perpendicular bisector of a triangle is a line (or ray or segment) that is perpendicular to a side of the triangle at the midpoint of the side. Perpendicular Bisector of a Triangle Perpendicular Bisector

  3. A point is equidistant from two figures if the point is the same distance from each figure. • Theorem 5.2 Perpendicular Bisector Theorem In a plane, if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

  4. Theorem 5.3 Converse of the Perpendicular Bisector Theorem: In a plane, if a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment. Ex.1: BD is the perpendicular bisector of AC. Find AD.

  5. Ex.2: In the diagram, WX is the perpendicular bisector of YZ. a. What segment lengths in the diagram are equal? b. Is V on WX?

  6. Ex.3: In the diagram, JK is the perpendicular bisector of NL. a. What segment lengths are equal? Explain your reasoning. b. Find NK. c. Explain why M is on JK?

  7. Ex.4: KM is the perpendicular bisector of JL. Find JK and ML.

  8. Concurrency • When three or more lines, rays, or segments intersect in the same point, they are called concurrent lines, rays, or segments. • The point of intersection of the lines, rays, or segments is called the point of concurrency.

  9. The three perpendicular bisectors of a triangle are concurrent. The point of concurrency may be inside the triangle, on the triangle, or outside the triangle. About concurrency 90° Angle-Right Triangle

  10. The three perpendicular bisectors of a triangle are concurrent. The point of concurrency may be inside the triangle, on the triangle, or outside the triangle. About concurrency Acute Angle-Acute Scalene Triangle

  11. The three perpendicular bisectors of a triangle are concurrent. The point of concurrency may be inside the triangle, on the triangle, or outside the triangle. About concurrency Obtuse Angle-Obtuse Scalene Triangle

  12. Theorem 5.4 Concurrency of Perpendicular Bisectors of a Triangle: The perpendicular bisectors of a triangle intersect at a point that is equidistant from the vertices of the triangle. • The point of concurrency (point of intersection) of the three perpendicular bisectors of a triangle is called the circumcenter of the triangle.

  13. FACILITIES PLANNING. A company plans to build a distribution center that is convenient to three of its major clients. The planners start by roughly locating the three clients on a sketch and finding the circumcenter of the triangle formed.

  14. Practice 2x = 5x – 6 0 = 3x – 6 6 = 3x x = 2 AB = 4 3x + 8 = 7x – 16 8 = 4x – 16 24 = 4x x = 6 AB = 26 6x + 11 = 11x – 9 11 = 5x – 9 20 = 5x x = 4 AB = 35

More Related