10854
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
The Midpoints of Two Cevians
A cevian is a line drawn from a vertex of a triangle to the opposite side.
Let ABC be a triangle and let M and N be the midpoints of the cevians BB' and CC'. Then the area of the quadrilateral BC'B'C is 4 times the area of AMN.
Contributed by:
Jay Warendorff
After work by:
Antonio Gutierrez
THINGS TO TRY
Drag Locators
SNAPSHOTS
DETAILS
The statement of the theorem is in
Problem 90. Quadrilateral and Triangle Areas, Midpoints
.
RELATED LINKS
Cevian
(
Wolfram
MathWorld
)
Midpoint
(
Wolfram
MathWorld
)
PERMANENT CITATION
"
The Midpoints of Two Cevians
" from
the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/TheMidpointsOfTwoCevians/
Contributed by:
Jay Warendorff
After work by:
Antonio Gutierrez
Share:
Embed Interactive Demonstration
New!
Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site.
More details »
Download Demonstration as CDF »
Download Author Code »
(preview »)
Files require
Wolfram
CDF Player
or
Mathematica
.
Related Demonstrations
More by Author
The Triangles Formed by the Endpoints and Midpoints of Cevians
Jay Warendorff
Two Midpoints of a Trapezoid
Jay Warendorff
Concurrency via Midpoints
Jay Warendorff
The Intersections of Extended Cevians with Three Circumcircles of Subtriangles
Jay Warendorff
Projections of Midpoints onto Circumradii
Jay Warendorff
Concyclic Points Derived from Midpoints of Altitudes
Jay Warendorff
Incircles and a Cevian
Jay Warendorff
Reflecting a Point through the Midpoints of a Triangle's Sides
Jay Warendorff
Perpendiculars from the Midpoints of the Orthic Triangle
Jay Warendorff
Concurrency Induced by a Cevian
Jay Warendorff
Related Topics
Plane Geometry
Triangles
Browse all topics
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to
Mathematica Player 7EX
I already have
Mathematica Player
or
Mathematica 7+