Explain

2. If a and b are constructible, give a geometric proof that ab is con- structible. (Hint: Consider the following figure. Notice that all seg- ments in the figure can be made with an unmarked straightedge and a compass.) 3. Prove that if c is a constructible number, then so is VIcl. (Hint: Consider the following semicircle with diameter 1 + [cl.) (This ex- ercise is referred to in Chapter 33.) d Icl 4. If a and b (b # 0) are constructible numbers, give a geometric proof that a/b is constructible. (Hint: Consider the following figure.) 5. Prove that sin 0 is constructible if and only if cos 0 is constructible. 6. Prove that an angle 0 is constructible if and only if sin 0 is con- structible. 7. Prove that cos 20 is constructible if and only if cos 0 is con- structible. 8. Prove that 30 is a constructible angle. 9. Prove that a 45 angle can be trisected with an unmarked straight- edge and a compass. 10. Prove that a 40 angle is not constructible. 11. Show that the point of intersection of two lines in the plane of a field Flies in the plane of F