When trying to prove a conjecture, first ask yourself if the statement appears to be true. Your approach to proving--or disproving--the statement will depend on whether you believe it to be true.
Later in this lesson, you will learn how to prove a conjecture in a very formal way that is somewhat unique to geometry. For now, though, practice deciding whether or not a conjecture appears to be true--and why you think so.
For each of the statements below, decide whether the conjecture is true. If it seems true, explain how someone might prove it. If it seems false, explain how someone might disprove it. When you have answered all of the questions, compare your answers to the suggested ones on the last screen.
I must pass at least one math class to graduate from high school.
All dogs have four legs.
The sum of two consecutive numbers will always be an odd number.
Two right angles are congruent.
| Your Responses | Sample Answers |
|---|---|
| Look at your school's graduation requirements. If the number of math credits needed for graduation is at least one, you have proved this conjecture. | |
| If just one dog is found that has only three legs, the conjecture is false. | |
| Any pair of consecutive numbers will include one even number and one odd number. The sum of an even number and an odd number is always odd. Therefore, this statement is true. | |
| The definition of a right angle is that it measures 90°. Two angles that have the same measurement are congruent, by definition. |
