Question 662167
<pre></i>You need a couple more statements.  Also, if you 
use < for an angle followed by a letter (not a number) you
must skip a space after < , otherwise the program will think 
it's an HTML tag and will delete what follows it. It's best 
to use the symbol &#8736; for an angle which is gotten by 
typing this code:

{{{"&#8736;"}}}.  
 

Given : m&#8736;1 = m&#8736;3 and m&#8736;2 = m&#8736;4
Prove : m&#8736;ABC = m&#8736;DEF

{{{drawing(300,300,-1,3,-1,3,
locate(.4,.2,1),red(arc(0,0,1.4,-1.4,0,30)),
locate(1.34,1.68,A),locate(-.14,.05,B),locate(2.05,.1,C),
locate(.45,.5,2),green(arc(0,0,1.7,-1.7,30,50),arc(0,0,1.8,-1.8,30,50)),
line(0,0,2,0),line(2cos(50*pi/180),2sin(50*pi/180),0,0), line(2cos(30*pi/180),2sin(30*pi/180),0,0) )}}}{{{drawing(300,300,-1,3,-1,3,
locate(.4,.2,3),red(arc(0,0,1.4,-1.4,0,30)),
locate(1.34,1.68,D),locate(-.14,.05,E),locate(2.05,.1,F),
locate(.45,.5,4),green(arc(0,0,1.7,-1.7,30,50),arc(0,0,1.8,-1.8,30,50)),
line(0,0,2,0),line(2cos(50*pi/180),2sin(50*pi/180),0,0), line(2cos(30*pi/180),2sin(30*pi/180),0,0) )}}}


Statements                Reasons 

1 m&#8736;1 = m&#8736;3               Given

2 m&#8736;2 = m&#8736;4               Given

3 m&#8736;1 + m&#8736;2 = m&#8736;3 + m&#8736;2  Equals (in step 1) added to equals 
                          (in step 2) gives equals.

4 m&#8736;1 + m&#8736;2 = m&#8736;3 + m&#8736;4  equals (in step 2) may be substituted
                          for each other (in step 3)

5 m&#8736;1 + m&#8736;2 = m&#8736;ABC      a whole is equal to the sum of its parts 

6 m&#8736;3 + m&#8736;4 = m&#8736;DEF      a whole is equal to the sum of its parts

7 m&#8736;ABC = m&#8736;DEF          equals (in steps 5 and 6) may be substituted 
                          for each other (in step 4).  

Edwin</pre>