Online Course Discussion Forum

Questions on II-A

 
 
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Questions on II-A
by Kevin Song - Saturday, 10 October 2020, 4:33 PM
 

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

 
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Re: Questions on II-A
by Dr. Kevin Wang - Saturday, 10 October 2020, 6:56 PM
 

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.

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Re: Questions on II-A
by Kevin Song - Sunday, 11 October 2020, 10:01 AM
 

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

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Re: Questions on II-A
by Dr. Kevin Wang - Sunday, 11 October 2020, 10:52 AM
 

Just carry it out and see if it works.