11405
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
15. Construct a Triangle Given the Lengths of Two Sides and the Median to the Third Side
This Demonstration shows a construction of a triangle
given the lengths
and
of the sides
and
and the length of the median
from
to
.
Construction
Let
be a line segment of length
and midpoint
.
Step 1: Draw a circle with center
and radius
and a circle with center
and radius
. Let
and
be the intersections of the two circles.
Step 2: Extend
to the point
such that
.
Verification
The triangle
has side
of length
.
and
bisect each other, so
is a parallelogram with sides
and
. The side
has length
, and the line segment
is the median from
of length
.
Contributed by:
Izidor Hafner
THINGS TO TRY
Slider Zoom
Gamepad Controls
Automatic Animation
SNAPSHOTS
DETAILS
With the condition
, the problem has a solution if and only if
[1, pp. 287–288].
Reference
[1] A. McFarland, J. McFarland and J. T. Smith, eds.,
Alfred Tarski: Early Work in Poland: Geometry and Teaching
, New York: Birkhäuser, 2014.
RELATED LINKS
Triangle
(
Wolfram
MathWorld
)
Median
(
Wolfram
MathWorld
)
PERMANENT CITATION
Izidor Hafner
"
15. Construct a Triangle Given the Lengths of Two Sides and the Median to the Third Side
"
http://demonstrations.wolfram.com/15ConstructATriangleGivenTheLengthsOfTwoSidesAndTheMedianToT/
Wolfram Demonstrations Project
Published: August 24, 2017
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
7. Construct a Triangle Given the Lengths of Two Sides and a Median of the Third Side
Izidor Hafner
8. Construct a Triangle Given the Lengths of Two Sides and the Length of the Altitude to One of Them
Izidor Hafner
13. Construct a Triangle Given the Length of Its Base, the Difference of the Base Angles and the Difference of the Lengths of the Other Two Sides
Izidor Hafner
14. Construct a Triangle Given the Length of the Altitude to the Base, a Base Angle and the Sum of the Lengths of the Other Two Sides
Izidor Hafner
9. Construct a Triangle Given the Length of Its Base, the Difference of the Base Angles and the Sum of the Other Two Sides
Izidor Hafner
5. Construct a Triangle Given Its Circumradius, the Difference of Base Angles and the Sum of the Other Two Sides
Izidor Hafner
17a. Construct a Triangle Given the Length of an Angle Bisector, the Angle at Another Vertex and Distance from the Third Vertex to the Angle Bisector
Izidor Hafner
17b. Construct a Triangle Given the Length of an Angle Bisector, the Angle at Another Vertex and the Distance from the Third Vertex to the Angle Bisector
Nada Razpet, Marko Razpet and Izidor Hafner
10. Construct a Triangle Given the Length of Its Base, the Difference of the Base Angles and the Slope of the Median to the Base
Izidor Hafner
6. Construct a Triangle Given Its Circumradius, Inradius and the Length of Its Base
Izidor Hafner
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+