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.

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Presentation transcript:

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 X Y AB XY is bisector of AB

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. A B C D X AX = XB

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

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

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.

X Y A B C Z ZBis an angle bisector. XM = MY

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