Let's see if you can look at a proof and determine which type of proof it is based on the type of evidence used to prove a conjecture. In the table below, read the conjecture in the left-hand column and the example proofs in the middle column, and decide whether each proof is formal or informal. Then click on the conjecture to check your answer.
| Conjecture | Proof | Formal or Informal? |
| Any integer multiple of the triple 3, 4, 5 will be a Pythagorean Triple. | Integer = 2 Multiply 3, 4, 5 by 2 to get 6, 8, 10. Test 6, 8, 10 to see if it is a Pythagorean Triple. 62 + 82 = 102 36 + 64 = 100 100 = 100 True Integer = 5 Multiply 3, 4, 5 by 5 to get 15, 20, 25. Test 15, 20, 25 to see if it is a Pythagorean Triple. 152 + 202 = 252 225 + 400 = 625 625 = 625 True These two examples show that the conjecture is probably true. |
Informal Proof |
| Any integer multiple of 3, 4, 5 will be a Pythagorean Triple. | Integer = x Multiply 3, 4, 5 by x to get 3x, 4x, 5x. Test 3x, 4x, 5x, to see if it is a Pythagorean Triple. (3x)2 + (4x)2 = (5x)2 9x2 + 16x2 = 25x2 25x2 = 25x2 This shows that the conjecture is always true. |
Formal Proof |
| All squares will have a perimeter that is 4 times the length of one side. | Square of length x has a perimeter equal to x + x + x + x = 4x This shows that the conjecture is always true. |
Formal Proof |
