Special Segments in Triangles Section 5 1 Perpendicular

Special Segments in Triangles Section 5 -1

Perpendicular Bisector a line or line segment that passes through the midpoint of a side of a triangle and is perpendicular to that side of the triangle XY is of AB X A Y B bisector

Theorem 5 -1 • Any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment.

Theorem 5 -2 • Any point equidistant from the endpoints of a segment lies on the perpendicular bisector of the segment.

CD is a perpendicular bisector of AB. C A X D AX = XB B

Median a segment that connects a vertex of a triangle to the midpoint of the side opposite that vertex. B BZ is a median. A Z C

Altitude a segment drawn from the vertex of a triangle perpendicular to the opposite side B A X BX is an altitude C

Theorem 5 -4 • Any point on the bisector of an angle is equidistant from the sides of the angle.

Theorem 5 -5 • Any point equidistant from the sides of an angle lies on the bisector of the angle.

ZB is an angle bisector. XM = MY Z A C M X Y B

Joke Time What tool do you use in Algebra? multi-pliers

There are 2 men on 2 different trains on the opposite sides of a 10 mile railroad track. One train is traveling 50 mph and the other train is traveling 40 mph. Where will they meet? in the hospital