Lines Associated with Triangles 4-3D

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Date: Sec 5-4 Concept: Medians and Altitudes of a Triangle

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Presentation transcript:

Lines Associated with Triangles 4-3D What is a centroid? What are concurrent lines? What is a point of concurrency? What are four lines associated with triangles?

Angle Bisector When an angle bisector is used in a triangle, it is a segment. The angle bisector cuts the angle in half and goes to the other side. A B C D Angle bisector

Median A median of a triangle is a segment whose endpoints are a vertex and the midpoint of the opposite side. (Goes from vertex to opposite side) F G H J Median

Altitude (height) An altitude of a triangle is a perpendicular segment drawn from a vertex to the line that contains the opposite side. (Vertex to opposite side at a right angle.) Altitude K L M N K L M N

Perpendicular Bisector A perpendicular bisector of a side of a triangle is a line perpendicular to a side through the midpoint of the side. (Perpendicular and bisects one side only) Perpendicular bisector B C A

Balancing Act Balance your triangle on the eraser end of your pencil. Mark the point. This is the centroid of the triangle. Use a ruler to find the midpoint of each side of your triangle. Draw all three medians. (Connect each vertex to the midpoint of the opposite side.) Do all three medians meet at one point? Measure the two segments of each median in your triangle. What do you find?

Concurrent Lines If three or more coplanar lines intersect at the same point, they are concurrent lines. The point of intersection is the point of concurrency. Concurrent lines Point of concurrency

Centroid The point of concurrency of the medians of any triangle is called the centroid. The centroid is the center of balance (or center of gravity) of the triangle. Centroid

Theorem The centroid of a triangle is located two-thirds of the distance from each vertex to the midpoint of the opposite side.

What is a centroid? The point of concurrency of the medians of any triangle is called the centroid. What are concurrent lines? If three or more coplanar lines intersect at the same point, they are concurrent lines. What is a point of concurrency? The point of intersection is the point of concurrency. What are four lines associated with triangles? Angle bisector, median, altitude, and perpendicular bisector.

Assignment 4-3D Page 307, 1-5, 7, 8, 12, 16-22