Geometry 5-3b Medians and Altitudes

Definitions 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

Investigation Calculators

Calculator 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

Median Concurrancy The three medians of a triangle are concurrent Centroid

Calculator Investigation 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?

Centroid Theorem 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.

Investigation 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

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

Summary

Practice

Homework Pages 260 – – 16, 20, 22, 27 – 29

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