5 1 Special Segments in Triangles Learn about

5. 1 Special Segments in Triangles • • Learn about Perpendicular Bisector Learn about Medians Learn about Altitude Learn about Angle Bisector

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

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

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

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

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

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

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 4 x + 10 = 90 4 x = 80 x = 20 BC = 2 x +(3 x - 4) BC = 40 + 56 = 96

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 )= 4 x- 6 2 x + 12 = 4 x - 6 2 x = 18 x=9 ABC = 4 x - 6 ABC = 30

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

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

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

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

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