Medians and Altitudes Geometry 5 3 b Median

Medians and Altitudes Geometry 5 -3 b

• Median of a triangle – a segment whose endpoints are a vertex and the midpoint of the opposite side • Altitude of a triangle – A perpendicular segment from a vertex to the line containing the opposite side of the triangle Definitions

• • • Supplies Patty Paper - 2 Straight Edge Compass Printer paper Investigation

• Draw a large triangle on your patty paper • Some students draw obtuse, some right, some acute Investigation

• Fold altitudes into each side of your triangle • Highlight the altitudes Investigation

• Are all the altitudes concurrent? Label and Save this piece of patty Paper Investigation

• The three altitudes of a triangle are concurrent Orthocenter Altitude Concurrancy Conjecture

• Calculators Investigation

• Turn the calculator ON, and start a new file • Home > 1 > no > • Open a graphs and geometry view window (3) Calculator Investigation

• Create a triangle, by connecting three line segments, label the segments CNR • Line segments are MENU > 7 > 5 • Add a label with Cntrl > Menu > 2 Calculator Investigation

• Construct the midpoints of each triangle side • Midpoints are MENU > A > 5 Calculator Investigation

• Construct medians, connecting midpoints to the opposite vertex • Segments are MENU > 7 > 5 Calculator Investigation

• Construct the intersecting points to find the centroid, label it T • Intersecting points are MENU > 7 > 3 Calculator Investigation

• The three medians of a triangle are concurrent Centroid Median Concurrancy

• Measure the short and the long part of a median • Measuring is MENU > 8 > 1 Calculator Investigation

• What do you notice about the two lengths? • Alter the shape of the triangle, does this still hold? Calculator Investigation

• The medians of a triangle are concurrent at a point that is two thirds the distance from each vertex to the midpoint of the opposite side. Centroid Theorem

• • Cardboard Scissors Ruler / Straight Edge Straightedge Investigation

• Cut out a scalene triangle • Draw all medians onto the triangle • Try balancing the cardboard triangle on your ruler edge, along a median Investigation

• Find the centroid for your triangle Investigation

• Try balancing your triangle on the eraser of your pencil at the centroid Investigation

• The centroid of a triangle is the center of gravity of the triangular region Center of Gravity

Summary

Practice

Practice

• Pages 260 – 262 • 11 – 16, 20, 22, 27 – 29 Homework

• Pages 260 – 262 • 11 – 16, 20, 22, 27 – 29, 34 Honors Homework