## Reasoning

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Task 1

a) Explore: Can you make the two angles the same? in the box below ?(if you drag the dots around you will see the shape changing)

b) Conjecture: Discuss what needs to happen for the angles to be equal

c) Conjecture: Answer Question 1 on the answers form

d) Convince: Can you explain why these angles are the same? Discuss, then answer Question 2 on the answers form.

We can now say that Corresponding Angles on parallel lines are always_______" Draw 2 examples of Corresponding angles on parallel lines

Task 1

a) Explore: Can you make the two angles the same? in the box below ?(if you drag the dots around you will see the shape changing)

b) Conjecture: Discuss what needs to happen for the angles to be equal

c) Conjecture: Answer Question 1 on the answers form

d) Convince: Can you explain why these angles are the same? Discuss, then answer Question 2 on the answers form.

**Write a note in your learning journal!**:__Axiom 1__: This arrangement of lines and angles is called**"Corresponding Angles"**We can now say that Corresponding Angles on parallel lines are always_______" Draw 2 examples of Corresponding angles on parallel lines

Task 2

Look at the Geogebra box below:

a) Explore When you move a black or purple line, think how it moves: Answer Question 3 in the answer form

b) Conjecture What can you say about how the lines are arranged? Question 4 in the answer form

b) Conjecture: Use the red and blue dots to move the lines around. Can you identify and angles that are always equal ?:

c) Explore: Using coloured pens and sheet 1, colour angles that are the same size with the same colour.

Extension: Are the angles always the same size when the lines are moved around with the blue and red dots? What changes and what stays the same?

d) Extension: Conjecture: What would make the angles not be the same any more? (type your answer in Question 5 on the Answer form)

Look at the Geogebra box below:

a) Explore When you move a black or purple line, think how it moves: Answer Question 3 in the answer form

b) Conjecture What can you say about how the lines are arranged? Question 4 in the answer form

b) Conjecture: Use the red and blue dots to move the lines around. Can you identify and angles that are always equal ?:

c) Explore: Using coloured pens and sheet 1, colour angles that are the same size with the same colour.

Extension: Are the angles always the same size when the lines are moved around with the blue and red dots? What changes and what stays the same?

d) Extension: Conjecture: What would make the angles not be the same any more? (type your answer in Question 5 on the Answer form)

*Task 3:*

Use the Geogebra Box below:

a) Explore: Can you make the angles the same?

b) Conjecture: what you did to make them the same? Answer in the answers form Question 6

c) Convince: Write a sentence that would convince someone that they are the same, Hint: use the axioms you have learned during this unit: Answer form Question 7

Write a note in your learning journal! :

__Axiom 2__: This arrangement of lines and angles is called

**"Alternate Angles"**

We can now say that Alternate Angles on parallel lines are always_______"

Task 4:

Using the Geogebra Box below:

a) Discuss: What can you say about lines f and g? (can you change how they are arranged by dragging them)

b) Explore: What is the same and what is different about the two angles when you drag the lines around? Write your conjecture in Answer Form Question 8

d) Convince: Can you explain why your conjecture is always true? in Answer form Question 9

Write a note in your learning journal! :

We can now say that Co-interior

Draw 2 examples of Co-interior Angles on Parallel Lines

Using the Geogebra Box below:

a) Discuss: What can you say about lines f and g? (can you change how they are arranged by dragging them)

b) Explore: What is the same and what is different about the two angles when you drag the lines around? Write your conjecture in Answer Form Question 8

d) Convince: Can you explain why your conjecture is always true? in Answer form Question 9

Write a note in your learning journal! :

__Axiom 3__: This arrangement of lines and angles is called**"Co-Interior Angles"**We can now say that Co-interior

*Angles on parallel lines always_______"*Draw 2 examples of Co-interior Angles on Parallel Lines

Task 5

Using the Geogebra Box Below

a) Explore: Someone says that Angles CAB, ABC and BCA add up to 180 degrees. Can you find 5 examples that show this is true? Draw the 5 examples in your learning journal and list them in Answer form Question 10

b)Conjecture: From doing these 5 examples have you shown it will always be true? Answer form Question 11

Using the Geogebra Box Below

a) Explore: Someone says that Angles CAB, ABC and BCA add up to 180 degrees. Can you find 5 examples that show this is true? Draw the 5 examples in your learning journal and list them in Answer form Question 10

b)Conjecture: From doing these 5 examples have you shown it will always be true? Answer form Question 11

Task 6: Generalising

Using the Geogebra Box Below and by drawing your own diagrams

a) Prove: Without measuring angles, can you use the axioms you have learned about angles to show that the angles in a triangle will always add to 180 degrees.

Write your proof in Answer form Question 12

Now write up your proof in your learning journal

Using the Geogebra Box Below and by drawing your own diagrams

a) Prove: Without measuring angles, can you use the axioms you have learned about angles to show that the angles in a triangle will always add to 180 degrees.

Write your proof in Answer form Question 12

Now write up your proof in your learning journal