Concurrent Lines within a Triangle How can you

Vocabulary Concurrent lines – Three or more lines that intersect at a common point.

Special Lines of a Triangle Angle Bisector Lines A line drawn from the vertex

Special Lines of a Triangle ¡ ¡ The point of concurrency is called the

Special Lines of a Triangle Perpendicular Bisector Lines A line drawn from the side

Special Lines of a Triangle ¡ ¡ ¡ The point of concurrency is called

Special Lines of a Triangle Some perpendicular bisector lines can be drawn from the

Special Lines of a Triangle Altitudes A line drawn from the vertex to the

Special Lines of a Triangle ¡ The point of concurrency is called the orthocenter.

Special Lines of a Triangle Median A line inside the triangle drawn from the

Special Lines of a Triangle The point of concurrency is called the centroid. The

Vocabulary ¡ ¡ ¡ Equidistant – Equal distance. Incenter – the point of concurrency

Vocabulary ¡ ¡ Centroid – the point of concurrency of the medians Circumcenter –

Special Lines The circumcenter is equidistant from the vertices of a triangle. The circumcenter

Special Lines The incenter is equidistant from each side of the triangle. The centroid

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Concurrent Lines within a Triangle How can you best describe the different lines within a triangle?

Vocabulary Concurrent lines – Three or more lines that intersect at a common point. Point of concurrency – The point where the lines intersect. Equidistant – Equal distance.

Special Lines of a Triangle Angle Bisector Lines A line drawn from the vertex of a triangle to the opposite side of a triangle. The angle bisector line bisects the angle from the vertex. There are three angle bisector lines.

Special Lines of a Triangle ¡ ¡ The point of concurrency is called the incenter. The incenter is equidistant to the sides and the line from them to the sides is perpendicular.

Special Lines of a Triangle Perpendicular Bisector Lines A line drawn from the side of one triangle to the opposite side. It bisects the side it’s drawn from and creates a 90 degree angle with that side. There are three perpendicular bisector lines for each triangle.

Special Lines of a Triangle ¡ ¡ ¡ The point of concurrency is called the circumcenter. The circumcenter is equidistant to the vertices of a triangle. It’s possible for the circumcenter to be located on or outside of the triangle.

Special Lines of a Triangle Some perpendicular bisector lines can be drawn from the vertex of a triangle. Only true with equilateral triangles and isosceles triangles.

Special Lines of a Triangle Altitudes A line drawn from the vertex to the opposite side. The altitude creates a right angle with the side. Some altitudes can be drawn outside of a triangle. Only obtuse triangles. There are three altitude lines.

Special Lines of a Triangle ¡ The point of concurrency is called the orthocenter.

Special Lines of a Triangle Median A line inside the triangle drawn from the vertex to the opposite side. The median bisects the opposite side. There are three median lines.

Special Lines of a Triangle The point of concurrency is called the centroid. The centroid is located 2/3 of the way from the vertex. The portion of the median from the centroid to the vertex is double the distance of the centroid the opposite side.

Vocabulary ¡ ¡ ¡ Equidistant – Equal distance. Incenter – the point of concurrency of the angle bisectors lines. Orthocenter – the point of concurrency of the altitudes.

Vocabulary ¡ ¡ Centroid – the point of concurrency of the medians Circumcenter – the point of concurrency of the perpendicular bisectors

Special Lines The circumcenter is equidistant from the vertices of a triangle. The circumcenter will meet on the outside of a triangle in an obtuse triangle. The circumcenter will meet on the triangle in a right triangle.

Special Lines The incenter is equidistant from each side of the triangle. The centroid is two-thirds the distance from each vertex to the midpoint of the opposite side.