2.  You can solve for a missing side of a right triangle.  You can tell if something is a right triangle.  You can make sure an angle is 90 degrees.

3.  a 2 +b 2 =c 2  The a and b represent the legs of the right triangle (it does not matter which one is which)  The C represents the hypotenuse and has to be where the hypotenuse is.  The hypotenuse is a cross from the 90 degree angle and is the longest side.

4.  First label the sides of the triangles with the a, b, and c  Then take the equation a 2 +b 2 =c 2 and substitute the values that are next to the given sides: b=4, a=3, and c=c  3 2 +4 2 =c 2, then use PEMDAS to simplify the equation before solving.  9+16=c 2, 25=c 2, then solve for the variable  25 = c 2 Square root both sides; c=5 3 4

5.  First label the sides of the triangle with a, b, and c  Then take the equation a 2 +b 2 =c 2 and substitute the values that are next to the given sides: a= 6, b=b, c=10  6 2 +b 2 =10 2, then use PEMDAS to simplify the equation before solving.  36+b 2 =100, then solve for the variable  36+b 2 -36=100-36, b 2 +0=64, b 2 = 64, b=8 6 10

6.  When given the values: a=9, b=12, c=15, just substitute the values given for each variable into the equation.  a 2 +b 2 =c 2 9 2 +12 2 =15 2 (substitute the values in) 81+144=225 225=225 (Simplify by following PEMDAS)  Since they are equal to each other at the end it is a right triangle, and that also means that one of the angles is 90 degrees  If the equation proves false in the end then that means that it is not a right triangle and none of the angles can be 90 degrees.