# 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

Initializing live version

Requires a Wolfram Notebook System

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

This Demonstration shows a construction of a triangle given the length of the base , the difference of the lengths of the other two sides and , and the difference of angles at the base.

[more]

Construction

Step 1: Draw a line of length and a circle with center and central angle over the chord . Measure out the point on the circle at distance from .

Step 2: Let the point be the intersection of and the right bisector of .

Then satisfies the given conditions.

Verification

Let and .

By construction, . By step 2, , so , the difference of the other sides.

Since the central angle by construction, . The line bisects the angle at . In any triangle, the , ; since is isosceles, . So and .

[less]

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

## Details

Reference

[1] D. S. Modic, Triangles, Constructions, Algebraic Solutions (in Slovenian), Ljubljana: Math Publishers, 2009 p. 95.

## Permanent Citation

Izidor Hafner

 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