Online Course Discussion Forum

Questions on II-A

 
 
SongKevin的头像
Questions on II-A
SongKevin - 2020年10月10日 Saturday 16:33
 

For 4.23, I don't know where to start, and would I use Heron's for 4.25?

 
WangDr. Kevin的头像
Re: Questions on II-A
WangDr. Kevin - 2020年10月10日 Saturday 18:56
 

Question 4.23 asks you to prove the converse of the Pythagorean Theorem.  So if you have a triangle $ABC$, whose side lengths satisfy the equation $a^2+b^2=c^2$, you want to prove that $\angle C=90^\circ$.  The idea to prove this result is to create a "helping" triangle $A'B'C'$, with $\angle C'=90^\circ$, and $a'=a$, $b'=b$.  Can you show that these two triangles are congruent?

For Question 4.25, if you are considering using Heron's formula, go ahead and try it out, and see if it works.

SongKevin的头像
Re: Questions on II-A
SongKevin - 2020年10月11日 Sunday 10:01
 

Can you use the Pythagorean Theorem for the helping triangle to show the hypotenuses are congruent, then use SSS?

WangDr. Kevin的头像
Re: Questions on II-A
WangDr. Kevin - 2020年10月11日 Sunday 10:52
 

Just carry it out and see if it works.