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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
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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
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