Section 5.1

21. B 22. A 23. C 24. F 25. D 26. E

5-2 Properties of Triangles

a line (or ray or segment) that is perpendicular bisector of a triangle --- a line (or ray or segment) that is perpendicular to a side of a triangle at the midpoint of the side. each triangle has 3 perpendicular bisectors – one for each side

Concurrent lines – three or more lines (or rays or segments) that intersect in the same point Point of concurrency – the point of intersection is called the point of concurrency The three perpendicular bisectors of a triangle are concurrent. The point of concurrency can be inside, on, or outside the triangle.

Circumcenter – the point of concurrency of the perpendicular bisectors of a triangle is called the circumcenter. Because the circumcenter is equidistant form the vertices, it is used as the center of a circumscribed circle. Circumscribed circle – a circle that goes around the outside of a polygon and intersects the polygon only at each vertex.

Angle bisector of a triangle – the bisector of an angle of the triangle. The three angle bisectors of a triangle are concurrent. The point of concurrency for the angle bisectors is called the incenter. The incenter is always inside the triangle.

The incenter is used as the center of an inscribed circle Inscribed circle – a circle inside a polygon that intersects the circle once on each side.