DO NOW Complete the 4 problems at the top of your worksheet. Problems 1 – 8 are for homework. Write your answer for the question below on the back of the worksheet. The Smith Construction Company has been hired to install a new water fountain at Winstonian Park. They would like to find the best location for the fountain so that the walking distance from each of the three main pieces of playground equipment is the same. How would they determine this point?

Perpendicular bisector Altitude Median Angle bisector

Construct an equilateral triangle

a given point on the line. Construct a line perpendicular to a given line through a given point on the line.

a given point not on the line. Construct a line perpendicular to a given line through a given point not on the line.

Perpendicular bisector

Angle bisectors B

Altitude

Median

POINTS OF CONCURRENCY

segments, or rays intersect A point of concurrency  is the point where THREE or more lines, segments, or rays intersect

POINTS OF CONCURRENCY In Triangles In-center Circumcenter Orthocenter Centroid

INCENTER is the point at which the angle bisectors of a triangle intersect.

The in-center is the point at which the angle bisectors of a triangle intersect. It is the center of the circle that can be inscribed in the triangle

CIRCUMCENTER is the point at which the three perpendicular bisectors of the sides of a triangle intersect.

The circumcenter is the point at which the three perpendicular bisectors of the sides of a triangle intersect. It is also the center of the circle circumscribed around a triangle. This circle passes through all three vertices of the triangle

of a triangle intersect. ORTHOCENTER is the point at which the three altitudes  of a triangle intersect. An altitude is a line segment that has an endpoint on the vertex of a triangle and is perpendicular to the side of the triangle that connects the other two vertices of the triangle.

of a triangle intersect. The orthocenter is the point at which the three altitudes  of a triangle intersect.

is the point at which the medians of a triangle intersect. CENTROID is the point at which the medians of a triangle intersect. Medians are the line segments that connect the midpoints of one side of a triangle to the opposite vertex in the triangle

The centroid is the point at which the medians of a triangle intersect. It is the center of gravity of the triangle.

The centroid is 2/3 of the distance from each vertex to the midpoint of the opposite side