1. Recall the conditions for whether or not 3 lengths can make a triangle.
The two shorter lengths must add up to be greater than the longest side length.
2. The 3rd side must be greater than some value and less than some value.
If I had two sides of 4 and a side of 6, the third side would have to be longer than 2. (If it was 2 or less, you would have 2+4=6, or 1.9+4<6, etc… which couldn’t make a valid triangle). The third side would also have to be less than 10 (If it was 10 or greater, 4+6=10, or 4+6<10.1, etc… which don’t meet the conditions of a valid triangle).
Note: 6-4=2, 6+4=10, and the third side “x,” in this case must be: 2<x<10
3. Smallest angle is across from the smallest side, middle angle is across from the middle side, and the largest angle is across from the largest side.
Smallest angle is opposite the smallest side, middle angle is opposite the middle side, and the largest angle is opposite the largest side.
Smallest angle opens up to the smallest side, middle angle opens up to the middle side, and the largest angle opens up to the largest side.
4. See HW 3 for help. Also remember the definition of Pythagorean Triples: 3 whole numbers that are solutions to the Pythagorean theorem. (No square roots around any of the 3 numbers, and all three numbers have to “work with” the Pythagorean theorem)
5. Refer to the work on your Hinge Theorem WS and your notes. Notice where the conditions for the Hinge theorem are being met in each diagram. Once you have two pairs of congruent sides, if you know the angles between those sides in both triangles, you can compare the third sides of each triangle, and vice versa.