Construct a scalene triangle AABC. Construct the altitudes, perpendicular bisectors and medians of a triangle. Determine the point of intersections of each of the three concurrency lines. On a separate sketch, delete all the concurrent lines, but keep the points of intersection. Show that these points of intersection are collinear. What do we call this line? Clearly indicate that the following are true, by naming and measuring your line egments: The centroid is always located between the circumcenter and the orthocenter. The centroid is twice as close to the circumcenter as to the orthocenter.
Construct a scalene triangle AABC. Construct the altitudes, perpendicular bisectors and medians of a triangle. Determine the point of intersections of each of the three concurrency lines. On a separate sketch, delete all the concurrent lines, but keep the points of intersection. Show that these points of intersection are collinear. What do we call this line? Clearly indicate that the following are true, by naming and measuring your line egments: The centroid is always located between the circumcenter and the orthocenter. The centroid is twice as close to the circumcenter as to the orthocenter.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Construct a scalene triangle AABC. Construct the altitudes, perpendicular bisectors
and medians of a triangle. Determine the point of intersections of each of the three
concurrency lines. On a separate sketch, delete all the concurrent lines, but keep the
points of intersection. Show that these points of intersection are collinear. What do
we call this line?
Clearly indicate that the following are true, by naming and measuring your line
segments:
a) The centroid is always located between the circumcenter and the orthocenter.
b) The centroid is twice as close to the circumcenter as to the orthocenter.
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Step 1: Sketching the Triangle
VIEWStep 2: Sketching the Altitudes
VIEWStep 3: Sketching Perpendicular Bisectors
VIEWStep 4: Sketching the Medians
VIEWStep 5: Drawing the Euler line passing through H, G, and P
VIEWStep 6: Comparing the distance between Orthocenter, Centroid, and Circumcenter
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