Chapter 13, Problem 68E

In Fig. 13-39 triangle BCD is a $72-72-36$ triangle with base of length 1 and longer side of length $x$ (Using this choice of values, the ratio of the longer side to the shorter side is $x/1=x$.)

a. Show that $x=\text{φ}$. (Hint: Triangle ACB is similar to triangle BCD.)

b. What are the interior angles of triangle DAB?

c. Show that in the isosceles triangle DAB, the ratio of the longer to the shorter side is also $\text{φ}$.

Figure 13-39