L1.19 - Evidence, Angles, and Proof
Learning Intentions and Success Criteria
[color=#ff0000]We are learning to:[/color][br][list][*]Label diagrams and explain conjectures (orally and in writing).[/*][/list][color=#ff0000]We are successful when we can:[/color][br][list][*]Label and make conjectures from diagrams.[/*][*]Prove vertical angles are congruent.[/*][/list]
19.1: Math Talk: Supplementary Angles
What do you notice? What do you wonder?
19.2: That Can’t Be Right, Can It?
Here is a figure where ray r meets line l. The dashed rays are angle bisectors.[br][list=1][*]Diego made the conjecture: “The angle formed between the angle bisectors is always a right angle, no matter what the angle between r and l is.” It is difficult to tell specifically which angles Diego is talking about in his conjecture. Label the diagram and rephrase Diego’s conjecture more precisely using your labels.[br][/*][*]Is the conjecture true? Explain your reasoning.[br][/*][/list]
19.3: Convince Me
Here are 2 intersecting lines that create 2 pairs of vertical angles:[br][list=1][*] What is the relationship between vertical angles? Write down a conjecture. Label the diagram to make it easier to write your conjecture precisely.[br][/*][*]How do you know your conjecture is true for all possible pairs of vertical angles? Explain your reasoning.[br][/*][/list]
Learning Intentions and Success Criteria
[color=#ff0000]We are learning to:[/color][br][list][*]Label diagrams and explain conjectures (orally and in writing).[/*][/list][color=#ff0000]We are successful when we can:[/color][br][list][*]Label and make conjectures from diagrams.[/*][*]Prove vertical angles are congruent.[/*][/list]
Cool-Down: Plead Your Case
Give the most convincing explanation you can for why a = c.