15. Construct a Triangle Given the Lengths of Two Sides and the Median to the Third Side

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

This Demonstration shows a construction of a triangle given the lengths and of the sides and and the length of the median from to .

[more]

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 .

[less]

Contributed by: Izidor Hafner (August 2017)
Open content licensed under CC BY-NC-SA


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.



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send