1. 5.1 Homework Quiz
What are the 4 ways of knowing that we discussed last time in class?
Find the measure of the missing angle in the diagram below assuming the figure is made up of 2 lines:
What are the minimal conditions necessary to identify that two triangles are congruent (one is just a transformation of the other)? Or in other words, what are the triangle congruence theorems?
108 ?
1 and 2 serve as a review of last class
3. This is a review of what students know from last year (they may need some help understanding these theorems because they may not know them at all)

2. Do you See What I See
Last time we looked at the figure below and imagined how it was constructed and then I showed you how it was constructed. The final diagram we said suggested that the sum of the angles of a triangle is 180 degrees.
Launch!

3. What can you say about the triangle in the following diagram
What can you say about the triangle in the following diagram? What convinces you that you can make this claim? Did you make any assumptions with this claim?
Sometimes we are asked to make conclusions from a diagram when we are given the last diagram in the sequence. Using this diagram I want you to take 3 minutes to answer these three questions.
Discuss what conjectures students made and label their ideas as conjectures.
*Emphasize that these are merely conjectures and that they are making some assumptions about the pictures in making their conjectures. What are some assumptions for conjecture a?
*At this point you are simply reasoning with a diagram.

4. List several conjectures that you believe are true about the triangles, quadrilateral, and diagonals of the quadrilateral in the figure below.
Have them come up with conjectures and list them on the board.
Since we have some information about the picture we can do more than just reason with a diagram, we can prove our conjectures.

5. What have we proven/accept as axioms?
Properties of the transformations: rotation, reflection, translation Any angles that together create a straight line, sum to 180 degrees. Triangle congruence theorems Pythagorean Theorem

6. Conjectures to be Proven
The base angles of isosceles triangles are congruent
The diagonals of a rhombus bisect each other
The diagonals of a rhombus are perpendicular
*Trick: Prove different triangles are congruent.
We need to split up into groups of 2 or three and each take one of these conjectures and work on proving them.
*split them into groups and have them prove the conjectures.
*Tell them a trick to doing it is to be able to justify that triangles DAC and DBC are congruent* Then they can use these to prove it!

7. What steps were used to create this diagram?
Give them a few minutes to work on their own and then talk about the steps they decided were used.
What steps were used to create this diagram?

8. Hannah and Abi were doing their math homework together
Hannah and Abi were doing their math homework together. One of the questions asks them to prove the following statement.
The points on the perpendicular bisector of a segment are equidistant from the endpoints of the segment.
They thought this diagram would be helpful for justification along with descriptions.
Read the situation together.
Pass out the descriptions that were created, and explain that they need to try to put these statements into notation you can remeber and remove unnecessary statements and reorganize them into the most logical order.
*Draw the diagram on the board for when you are investigating the argument.

9. Just need to pick an arbitrary point C on l.
Given information
Just need to pick an arbitrary point C on l.
Restating goal
Construct line segments AC and BC to create triangles.
Thinking. Not necessary for the argument
It might be easier to order these statements by talking about the angle measure in between the two sides.
Walk them through my reasoning on this proof.
We need to name the two triangles that are congruent
A and B are equidistant from C

11. What have we proven:
-Properties of the transformations -Any angles that create a straight line total 180 degrees. -Triangle congruence theorems -Pythagorean Theorem *The base angles of isosceles triangles are congruent. *The diagonals of a rhombus bisect each other. *The diagonals of a rhombus are perpendicular. *The points on the perpendicular bisector of a segment are equidistant from the endpoints of the segment.