Question

List the sides of each triangle from shortest to greatest

Answer 1

In every triangle, the largest side, is opposite the largest angle.

Also, the smallest side, is opposite the smallest angle.


a.$70^o\ \textgreater \ 60^o\ \textgreater \ 50^o$ so $|RQ|\ \textgreater \ |PR|\ \textgreater \ |PQ|$, 

because RQ is opposite angle P, the largest,
PR is opposite angle Q , the middle
and PQ is opposite angle R, the smallest.

Greatest side: RQ


b. The sum of the measures of the interior angles of any triangle is 180°, 

so 

$m(A)+m(B)+m(C)=180^o\\\\50^o+45^o+x=180^o\\\\x=180^o-50^o-45^o=85^o$

thus, m(C) is the largest angle. This means the largest side is the side AB.



Answers:

a) RQ
b)AB