1. Midsegment Review Find the Value of X and Identify all Parallel Lines

2. Section 5.2 Perpendicular Bisectors and Triangles Main Idea: Be able to find and use the Circumcenter of a Triangle to solve problems

3. 1.intersects a given segment at a 90° angle, and 2.passes through the given segment's midpoint

4. Finding the perpendicular bisectors of a triangle by folding. 1.Use the triangle Image I have given you 2.Pick one side of the triangle 3.Holding the paper up to the light, fold the paper so that the side vertices line up perfectly 4.Fold the entire sheet 5.Open the paper and use a ruler to assure yourself that the folded line goes through the midpoint of your chosen side 6.Pick any point on the folded line and measure the distance from that line to the end point of the side you chose 7.What do you find?

5. Theorem 5.2: Perpendicular Bisector Theorem

6. Prove the Perpendicular Bisector Theorem StatementsReasons 1. Given 2. Definition of Bisector 4. Reflexive Property 5. SAS 6. CPCTC

7. Theorem 5.3: Converse of the Perpendicular Bisector Theorem

8. Using Perpendicular Bisectors: Example Problems C P A B 7 8 1. 2. 3. _______________

9. Finding the Circumcenter of a triangle by folding. 1.Use the triangle Image I have given you 2.Pick another side of the triangle 3.Holding the paper up to the light, fold the paper so that the side vertices line up perfectly 4.Fold the entire sheet 5.Repeat the process for the last side 6.Draw a point where the three lines cross. 7.Measure the distance from that point to each of the vertices 8.What do you find?

10. Theorem 5.4: Concurrency of Perpendicular Bisectors of a Triangle

11. Circumcenter of a Triangle The Circumcenter of a Triangle is equidistant from the three vertices. Therefore the circumcenter is the center of a circle that passes through all three vertices