 Welcome, geometricians and logicians to some conjecture practice. You should have your note sheet out and we will be working on some of the conjectures listed on your sheet. The instructions state that we are to determine whether each conjecture is true or false. And if it is false, find a counter example. Our first conjecture is that the sum of two odd integers is even. Try and find two odd numbers that when you add them together, do you always get an even? Or do you sometimes get an odd? Pause the video right now and practice. This conjecture is true, no matter what odd integers you try when you add two odd integers. The answer is indeed even. Our next conjecture is that the product of an odd integer and an even integer is odd. Use an odd integer and an even integer and multiply them together and see what kind of answer you get. This conjecture is false and a counter example is that six times seven is 42. Six being an even integer, seven being an odd integer, when I multiply them I get 42. The conjecture is false and I have provided a counter example of that. The instructions on the next part of the note sheet state that you are to make a conjecture based on the given information. You have some information, you are supposed to make a conjecture and draw a figure to illustrate the conjecture. Pause the video right now and make a conjecture. Maybe make two conjectures about the information if you know that angle ABC is a right angle. What else do you know? So here is my illustration, I drew a picture, a figure to illustrate my conjecture. I might conjecture that angle ABC is a 90 degree angle or I might have a conjecture that segment AB and BC are perpendicular. So those are two examples of conjectures that I can make from the information that angle ABC is a right angle. Now I have the conjecture that point S is between R and T. Draw the figure of S between R and T and make a conjecture based on that figure. So here is my figure, S is between R and T. A conjecture might be that distance RS plus distance ST equals distance RT. If you remember segment addition from chapter one from back about a week ago. Looking at the note sheet our next set of instructions say determine whether each conjecture is true or false. If it's true you're done. If it's false you need to give a counter example for the false conjecture. We have that angles one and two are adjacent and the conjecture is that angle one and two form a linear pair. Is it true that if two angles are adjacent they absolutely have to form a linear pair. No that is not true this is a false conjecture. Now I will draw a counter example. So here's a picture of angle one and angle two they are adjacent they do have share a common side but they certainly do not form a line. So that is a counter example to the conjecture that they must be a linear pair. They can be adjacent without being a linear pair. Our next conjecture is that given ST and U collinear and the distance ST equals the distance TU. Is it true that T has to be the midpoint of SU? Think about that for a minute maybe draw a picture if you need to see what you think. This conjecture is true so we state it is true we don't have to find a counter example because there is none. This is a true conjecture. Now complete the third example of given and a conjecture on your own determine whether it's true or false and if it's false draw a counter example. I can't wait to see what you come up with in class tomorrow.