1. 5.3: Concurrent Lines, Medians and Altitudes Objectives: Students will be able to… Identify properties of perpendicular bisectors and angle bisectors Identify properties of medians and altitudes of triangles

2. Vocabulary Concurrent: 3 or more lines intersect at a point Point of Concurrency: where the lines intersect

3. Median of a Triangle A segment whose endpoints are a vertex of a triangle and the midpoint of the opposite side

4. Altitude of a Triangle The perpendicular segment from the vertex to the line containing the opposite side Acute Triangle: Inside Right Triangle: Side Obtuse Triangle: Outside

5. Special Triangle Segments Name of SegmentPicture Point of Concurrency Theorem and /or fact about Point of Concurrency Perpendicular Bisectors Angle Bisectors Medians Altitudes Circumcenter The circumcenter is equidistant from the vertices of the triangle Incenter The incenter is equidistant to the sides of the triangle.

6. Example: Find the values of the variables. y 4 x 10