 # 24a. Construct a Triangle Given the Length of the Altitude to the Base, the Difference of Base Angles and the Sum of the Lengths of the Other 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 marked-ruler (or verging) construction of a triangle given the length of the altitude to the base, the difference of angles at the base and the sum of the lengths of the other two sides.

[more]

Construction

From a point draw two rays and at an angle .

Let be on such that . Let be the intersection of the angle bisector of the angle and the perpendicular to at . Thus and is a right triangle with hypotenuse .

Draw the line segment of length with between and and on .

Move along until is on ; call this point . Then set .

Let be the reflection of in .

Then satisfies the stated conditions.

Proof

In the triangle , , , but the exterior angle , so .

Triangles and are congruent, so , and .

[less]

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

## Snapshots   ## Details

This is a verging, or marked-ruler construction. For verging, see [1, p. 124].

Reference

 G. E. Martin, Geometric Constructions, New York: Springer, 1998.

## 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