For Thursday: 5.6 investigation on p. 273 steps 1-8, and on p. 276: 1-7, 9
To be assigned on Thursday due when we return
5.7 on p. 282: 1-5, 8, 10
5.8 on p. 289: 1-5, 7
Assignment: Complete your Chapter 4 Reasoning Assessment and be ready to hand it in at the beginning of class.
Assignment: No HW tonight – tomorrow we will work on creating the videos, graphs and presentations for Thursday/Friday.
Tuesday, 13 December 2016
I was informed that I was incorrect when I predicted 100% chance of school for last Thursday. The question is why would I have been wrong even if we had in fact had school last Thursday. If I said 100% chance of school and then school happens surely my estimate was correct. Anyway, I hope you stayed warm or found a way to enjoy the cold!
Friday, 2 December 2016
* What is the significance of the arrows in a flow proof?
* What are some different ways you could organize this flow proof into a 2-column proof?
* Arrows are used to indicate when one statement follows from another. The arrow shows the order of the logic.
* Statements could, arguably be put into many different orderings so long as no statement comes before a statement which pointed to it in the flow proof. So there are many ways to arrange these statements into a valid proof, it would be preferable to set up the statements so that one line of reasoning is presented without interruption.
Thursday, 1 December 2016
- Clear question or statement to be proved
- Multiple well labeled, helpful diagrams. Especially useful when isolating an important triangle out of a figure in which many triangles overlap.
- Every statement is supported by a reason (and also proof indicates if a reason follows from some other statement)
- The proof has a logical structure in which there are no gaps in reasoning, each statement follows from the previous statements or stands on its own.
- The proof ends with the statement we desired to prove at the outset.
Assignment: 4.6 on p. 231: complete 1-12 (you may skip the two problems your group worked on together)
Pictures of student's proofs.
Assignment: previously assigned sections 5.1 – 5.4 + practice quiz w/s
Assignment: Study for the Mod 2 test tomorrow.
Assignment: 4.6 on p. 231: 1-4
Questions all apply to this figure
1. Are angles 1 and 2 congruent in the figure?
2. Are angles 3 and 4 congruent in the figure?
3. What else would you need to know in order to prove triangle ABD and triangle CDB are congruent?
1. Yes, angles 1 and 2 are congruent because they are alternate interior angles formed by parallel lines CB and AD and the transversal BD.
2. Cannot be determined. Since we do not know if CD and AB are parallel, we cannot say whether or not angles 3 and 4 are congruent. To avoid doing assuming we can eyeball parallel lines you could imagine the shape with AD still parallel to segment BC but if BC and AD are different lengths angle 3 and 4 can have different measurements.
3. Many possible answers. Here are a few
- If we knew that BC = AD we could prove the triangles congruent by SAS.
- If we knew that angle 3 and 4 were congruent, we could use ASA
- If we knew that angle C and angle A were congruent, we could use AAS.