The "If -Then" theorem please answer this 4 question #1:equilateral triangles are isosceles #2: The square of an even integer is even

Question

#3:The sum of two consecutive integers id odd and #4: Every terminating decimal is a rational number. Thank you so much. For my assignment this day. 

Answer 1

#1)   If equilateral then it is isosceles triangle.   

         

               Equilateral triangles have 3 equal sides. Isosceles triangles have 2 equal sides.

               Hence equilateral automatically guarantees isosceles.

 

#2)  If the integer is even then it's square is even.

 

        Proof:  X is even.   Then x=2n for some integer n.

                 x^2 = 4n^2 which is also an even integer

 

 #3) If x and y are consecutive integers then their sum is odd.

   Proof:  y = x=1 since they are consecutive integers.

               X+y = x+(x+1) = 2x + 1 which is odd

 

#4)  If the number can be expanded into a terminating decimal then it is rational.

       Proof:  the number can be written as a terminating decimal which then can be written as a fraction,

                   whose denominator shall be some power of 10