I want to determine if a triangle is a (unique triangle) or a (no triangle) or (more than one triangle)

Question

My question is linked to math and its a 7th grader question

Answer 1

Hello, Devin,

If I give you the length of two sides of a triangle with an an angle between the sides given, such as side-angle-side, the triangle will make a unique triangle (one of a kind) by the side-angle-side postulate.

              \5in

_____ 50^°\                 side-angle-side postulate (basic principle)

     10 in.

 

 

If you are given two angles and the length of a side between the angles, then you have a unique triangle(You can't make more than this kind of triangle.)

 

       ^/80°_______80°_\

 

If you are given side-side-side of a triangle,  for example, 6 inches by 8 inches by 12, you will need to check further by adding the shorter legs together.  Their sum should be longer than the length of the longest side.

 

        |            \

    6  |              \12                   6 + 8 (is greater than)>12                  Unique triangle is made.

        |_________\                        14>12

             8

 

However, when you are given three angles, you can make other triangles (infinitely many) with the same three angles, but their lengths would be similar.  Some could be bigger and some smaller, but all with the same side angle measures.

I hope that I have helped giving you this information.  Susan C.