Question 173746
<pre>
{{{drawing(400,425,-2.5,2.5,-1,4,

triangle(-1,0,1,0,0,3.077683537),
triangle(1,0,1.618033989,1.902113033,-1.618033989,1.902113033),
triangle(1.618033989,1.902113033,0,3.077683537,-1,0),
triangle(0,3.077683537,-1.618033989,1.902113033,1,0),
triangle(-1.618033989,1.902113033,1.618033989,1.902113033,-1,0),
locate(0,3.3,D),locate(1.6,2.2,C),locate(-1.6,2.2,E),
locate(-1,-.05,A),locate(1,-.05,B) 
)}}}

1. The sum of the interior        (n-2)*180° = (5-2)*180° =
angles is 540°                    3*180° = 540°

2. <font face = "symbol">Ð</font>ABC = 72°                     All interior angles of a regular 
                                  polygon are equal, and 540°÷5=72°

3. AB = BC                        All sides of a regular polygon 
                                  are equal. 

4. <font face = "symbol">D</font>ABC is isosceles              Two sides equal, AB = BC      
                               
5. <font face = "symbol">Ð</font>BAC+<font face = "symbol">Ð</font>BCA+<font face = "symbol">Ð</font>ABC=180°            The sum of the interior angles
                                  of a triangle is 180°

6. <font face = "symbol">Ð</font>BAC+<font face = "symbol">Ð</font>BCA+108°=180°            Substituting 72° for <font face = "symbol">Ð</font>ABC, since
                                  they are equal.

7. <font face = "symbol">Ð</font>BAC+<font face = "symbol">Ð</font>BCA=72°                  Subtracting equals from equals,
                                  (subtract 108° from both sides)

8. <font face = "symbol">Ð</font>BAC = <font face = "symbol">Ð</font>BCA                    Base angles of isoceles <font face = "symbol">D</font>ABC

9. <font face = "symbol">Ð</font>BAC = <font face = "symbol">Ð</font>BCA = 36°              Equal angles, each half of 72°, from 7


10. <font face = "symbol">Ð</font>CDE = 72°                     All interior angles of a regular 
                                   polygon are equal, and 540°÷5=72°

11. CD = DE                        All sides of a regular polygon 
                                   are equal. 

12. <font face = "symbol">D</font>CDE is isosceles              Two sides equal, CD = DE      
                               
13. <font face = "symbol">Ð</font>DCE+<font face = "symbol">Ð</font>DEC+<font face = "symbol">Ð</font>CDE=180°            The sum of the interior angles
                                   of a triangle is 180°

14. <font face = "symbol">Ð</font>DCE+<font face = "symbol">Ð</font>DEC+108°=180°           Substituting 72° for <font face = "symbol">Ð</font>CDE, since
                                  they are equal.

15. <font face = "symbol">Ð</font>DCE+<font face = "symbol">Ð</font>DEC=72°                 Subtracting equals from equals,
                                  (subtract 108° from both sides)

16. <font face = "symbol">Ð</font>DCE = <font face = "symbol">Ð</font>DEC                    Base angles of isoceles triangle CDE

17. <font face = "symbol">Ð</font>DCE = <font face = "symbol">Ð</font>DEC = 36°              Equal angles, each half of 72°, from 15.

18. <font face = "symbol">Ð</font>BCA = 36°                     From 9.

19. <font face = "symbol">Ð</font>DCE = 36°                     From 17.

20. <font face = "symbol">Ð</font>BCA+<font face = "symbol">Ð</font>ACE+<font face = "symbol">Ð</font>DCE = <font face = "symbol">Ð</font>BCD          Whole = sum of parts.

21. <font face = "symbol">Ð</font>BCD = 108°                    Reason 2

22. <font face = "symbol">Ð</font>BCA+<font face = "symbol">Ð</font>ACE+<font face = "symbol">Ð</font>DCE = 108°          Substituting equals for equals

23. 36° + <font face = "symbol">Ð</font>ACE + 36° = 108°        Subs. equals for equals, using
                                   18 and 19.

24. 72° + <font face = "symbol">Ð</font>ACE = 108°              Adding 36°+36° in 22.

25. <font face = "symbol">Ð</font>ACE = 36°                     Subtract equals from equals.
                                   (Subtract 72° from both sides of 25.
26. <font face = "symbol">Ð</font>BAC = 36°                     Step 9

27. <font face = "symbol">Ð</font>ACE = <font face = "symbol">Ð</font>BAC                    Both equal 36°

28. EC <font face = "symbol">ú÷</font> AB                       Equal alternate interior angles <font face = "symbol">Ð</font>ACE and
                                   <font face = "symbol">Ð</font>BAC when transversal AC cuts lines
                                   EC and AB
Edwin</pre>