A Construction for

Strategies and Hints

  1. has the same measure as . And, the Pythagorean Theorem can be used to find AC from AB and BC. AD = AC 1.3287682

  2. , , and also form a right triangle. By the Pythagorean Theorem,
    AE     1.4197271.

  3. The similar triangles FED and DEA give the following proportion:



    The students just computed AE. Since ED = 0.5, FE 0.176902. To get AF, subtract FE from AE: 1.4198281 - 0.176092 = 1.2436369. So, AF 1.2436369.

  4. The two similar triangles are AFB and AEG.



They give the following proportion:



Since AF and AE have been found, and AB = 1, AG 1.1415929.

Solution

The final step is to subtract AB from AG to get BG: 1.1415929 - 1 = 0.1415929.