1. Create a line segment that connects A and C.[br]2. Place a point where the two circles meet. (Pick one intersection point not both). Label this point E.[br]3. Construct a line segment that connects A and E and then another line segment that connects C and E.[br]4. Use the cm tool to measure the length of each side of your triangle.
Please record the length of AC AE, and CE.
What is the length of AE+CE?
What do you notice about AE+CE compared to AC?
Drag point C above to make AC longer. What eventually happens to your triangle? Why do you think this happens?
What is the measure of the following angles?[br]m<A = _____[br]m<C = _____[br]m<E = _____
Fill in the blanks:[br]AC is opposite angle ______[br]AE is opposite angle ______[br]CE is opposite angle ______
What conjecture can you make about side lengths and their opposite angles?