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Using Postulates and/or Theorems, determine whether PRQ ~ MRN. Show all your work and explain why the triangles are similar or why they are not. 

 Feb 15, 2018

Best Answer 

 #1
avatar+7347 
+3

Both triangles have a 90° angle. In order for the triangles to be similar, the sides that form this angle must be proportional, by the SAS Similarity Theorem.

 

If  △PRQ ~ △MRN , then  PR / RQ  =  MR / RN

 

Is it true that   PR / RQ  =  MR / RN   ?

 

PR / RQ  \(\stackrel{?}{=}\)  MR / RN

                                       Plug in the lengths of PR, RQ, MR, and RN.

12 / 18  \(\stackrel{?}{=}\)  8 / 6

                                      Reduce  12/18  by  3 .

4 / 6   \(\stackrel{?}{=}\)   8 / 6

 

4 / 6   ≠   8 / 6

 

Therefore  △PRQ  is not similar to   △MRN

 Feb 15, 2018
 #1
avatar+7347 
+3
Best Answer

Both triangles have a 90° angle. In order for the triangles to be similar, the sides that form this angle must be proportional, by the SAS Similarity Theorem.

 

If  △PRQ ~ △MRN , then  PR / RQ  =  MR / RN

 

Is it true that   PR / RQ  =  MR / RN   ?

 

PR / RQ  \(\stackrel{?}{=}\)  MR / RN

                                       Plug in the lengths of PR, RQ, MR, and RN.

12 / 18  \(\stackrel{?}{=}\)  8 / 6

                                      Reduce  12/18  by  3 .

4 / 6   \(\stackrel{?}{=}\)   8 / 6

 

4 / 6   ≠   8 / 6

 

Therefore  △PRQ  is not similar to   △MRN

hectictar Feb 15, 2018

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