1. 5.1 Special Segments in Triangles Learn about Perpendicular Bisector Learn about Medians Learn about Altitude Learn about Angle Bisector

2. Definitions: Perpendicular Bisector A line that passes through the midpoint of a side of a triangle and is perpendicular to same side. Median A line segment that connects a vertex of triangle with its opposite side midpoint

3. Definitions Altitude A line segment with one end point at a vertex and other perpendicular to its opposite side Angle Bisector: A line segment that divides a given angle into two equal halves

4. Perpendicular Bisector A line that passes through the midpoint of a side of a triangle and is perpendicular to that side.

5. Median A line segment that connects a vertex of triangle with its opposite side midpoint

6. Altitude A line segment with one end point at a vertex and other perpendicular to its opposite side

7. Angle Bisector A line segment that divides a given angle into two equal halves

8. Solution: Median: A line segment that connects a vertex of triangle with its opposite side midpoint

9. Example: Given Altitude Solve for x: Solution: Altitude: A line segment with one end point at a vertex and other perpendicular to its opposite side 4x + 10 = 90 4x = 80 x = 20 BC = 2x +(3x - 4) BC = 40 + 56 = 96

10. Example: Given Angle Bisector Solve for x: Solution: Angle Bisector: A line segment that divides a given angle into two equal halves 2( x + 6 )= 4x- 6 2x + 12 = 4x - 6 2x = 18 x = 9 ABC = 4x - 6 ABC = 30

11. Example: Given Angle Bisector Solve for x: Solution: Angle Bisector: A line segment that divides a given angle into two equal halves 6x + 3 = 5x + 9 x + 3 = 9 X = 6

12. Example: Given Angle Bisector Solve for x: Solution: Angle Bisector: A line segment that divides a given angle into two equal halves 2(3x – 7) = 4x 6x -14 = 4x 2x = 14 X = 7

13. Example: Given Median Solve for x: Solution: Median: A line segment that connects a vertex of triangle with its opposite side midpoint 2(5x – 3) = 8x 10x - 6 = 8x 2x = 6 X = 3

14. Example: Given Median Solve for x: Solution: Median: A line segment that connects a vertex of triangle with its opposite side midpoint x – 4 = 2x- 10 - 4 = x - 10 x = 6

15. Example: Given Median Solve for x: Solution: Median: A line segment that connects a vertex of triangle with its opposite side midpoint x + 3 = 2x - 17 3 = x - 17 x = 20 AB = 20- 7 AB = 13