1. Learning Goal:  IWBAT to solve for unknown side lengths and angles in triangles by using theorems about triangles. Homework :  HW 3.8: Midsegment Theorem Worksheet ------------------------------------------------------------------- Do Now:  Find the value of x in the exercises below. September 23, 2013 1) Sit. 2) Materials out. 3) Backpacks away. 4) Do Now SILENTLY.

2. Agenda: 1.Do Now (10 min) 2.H-L Congruence Theorem (10 min) 3.Midsegment Theorem (30 min) 4.Isosceles Triangles (25 min) 5.Congruent Triangles (15 min) 6.Closure (5 min)

3. Retake Quizzes:  10 th and 11 th graders can take retakes for any quiz we have taken so far.  You will be required to complete an error analysis sheet on the quiz you plan to retake.  Arrive to the retake sessions below with your error analysis sheet as the entry ticket. Mr. Rivera: Monday, Sept 23 (3:30 – 4:45pm) Ms. Walzberg: Wednesday, Sept 25 (7:00am)  If you cannot make these sessions, let us know ASAP.

4. Explore Congruence of Right Triangles  Right triangles consist of two legs, a hypotenuse, and a 90° angle. Task 1: Determine whether the following statement is true or false. Justify your response with a proof or counterexample.  If the hypotenuse of a right triangle is the same length as the hypotenuse of another right triangle, then the triangles MUST be congruent.

5. Explore Congruence of Right Triangles Task 1: If the hypotenuse of a right triangle is the same length as the hypotenuse of another right triangle, then the triangles MUST be congruent. FALSE Note that both right triangles have a hypotenuse with length 6 cm, but are NOT congruent.

6. Explore Congruence of Right Triangles  Right triangles consist of two legs, a hypotenuse, and a 90° angle. Task 2: Determine whether the following statement is true or false. Justify your response with a proof or counterexample.  If two legs of a right triangle are the same length as two legs of another right triangle, then the triangles MUST be congruent.

7. Explore Congruence of Right Triangles  Right triangles consist of two legs, a hypotenuse, and a 90° angle. Task 2: Determine whether the following statement is true or false. Justify your response with a proof or counterexample.  If two legs of a right triangle are the same length as two legs of another right triangle, then the triangles MUST be congruent. TRUE by SAS Congruence Postulate AKA Leg-Leg Congruence Theorem.

8. Explore Congruence of Right Triangles  Right triangles consist of two legs, a hypotenuse, and a 90° angle. Task 3: Determine whether the following statement is true or false. Justify your response with a proof or counterexample.  If the hypotenuse and one leg of a right triangle are the same length as the hypotenuse and one leg of another right triangle, then the triangles MUST be congruent.

9. Explore Congruence of Right Triangles  Task 3: If the hypotenuse and one leg of a right triangle are the same length as the hypotenuse and one leg of another right triangle, then the triangles MUST be congruent. No matter how I rearrange the hypotenuse and leg, I will always get the same right triangle. TRUE

10. Hypotenuse-Leg Congruence Theorem  If the hypotenuse and leg of one right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent (Figure 3-28).

11. Hypotenuse-Leg Congruence Theorem Are the following pairs of triangles congruent? If they are, justify your response with a congruence theorem.

12. Exploring the Midsegment of a Triangle  A midsegment of a triangle is a segment that connects the midpoints of two sides of a triangle.

13. Exploring the Midsegment of a Triangle  Now select a midsegment from your triangle and measure its length in centimeters using a ruler.  Select the side of the triangle that is parallel to the midsegment you selected. Measure the length of that side in centimeters.  What did you notice about the lengths of the midsegment and the length of the side parallel to the midsegment?

14. Midsegment Theorem  Now select a midsegment from your triangle and measure its length in centimeters using a ruler.  Select the side of the triangle that is parallel to the midsegment you selected. Measure the length of that side in centimeters.  What did you notice about the lengths of the midsegment and the length of the side parallel to the midsegment?

15. Midsegment Theorem Activity  Students work in pairs. Each pair receives a whiteboard, marker, and eraser.  Teacher will present practice exercises about the midsegment theorem on the board.  Your teams have a few minutes to solve the problem and write the answer on the whiteboard with its justification.  Display your whiteboard when the timer runs out.

16. Midsegment Theorem – Exercise 1  Find the missing length indicated.

17. Midsegment Theorem – Exercise 2  Find the missing length indicated.

18. Midsegment Theorem – Exercise 3  Find the missing length indicated.

19. Midsegment Theorem – Exercise 4  Solve for x.

20. Midsegment Theorem – Exercise 5  Solve for x.

21. Midsegment Theorem – Exercise 6  Solve for x.

22. Midsegment Theorem – Exercise 7  Solve for x.

23. Isosceles Triangles Activity  Students work in pairs. Each pair receives a whiteboard, marker, and eraser.  Teacher will present practice exercises about isosceles triangles on the board.  Your teams have a few minutes to solve the problem and write the answer on the whiteboard with its justification.  Display your whiteboard when the timer runs out.

24. Isosceles Triangles – Exercise #1  Find the value of x.

25. Isosceles Triangles – Exercise #2  Find the value of x.

26. Isosceles Triangles – Exercise #3  Find the value of x.

27. Isosceles Triangles – Exercise #4  Find the value of x.

28. Isosceles Triangles – Exercise #5  Find the value of x.

29. Isosceles Triangles – Exercise #6  Find the value of x.

30. Isosceles Triangles – Exercise #7  Find the value of x.

31. Isosceles Triangles – Exercise #8  Find the value of x.

32. Isosceles Triangles – Exercise #9  Find the value of x.

33. Isosceles Triangles – Exercise #10  Find the value of x.

34. Triangle Congruence Activity  Students work in pairs. Each pair receives a whiteboard, marker, and eraser.  Teacher will present practice exercises about the congruence of triangles on the board.  Your teams have 1 minute to solve the problem and write the answer on the whiteboard with its justification.  Display your whiteboard when the timer runs out.

35. Exercise #1  State if the two triangles are congruent? If they are, justify your answer with a congruence postulate or theorem.

36. Exercise #2  State if the two triangles are congruent? If they are, justify your answer with a congruence postulate or theorem.

37. Exercise #3  State if the two triangles are congruent? If they are, justify your answer with a congruence postulate or theorem.

38. Exercise #4  State if the two triangles are congruent? If they are, justify your answer with a congruence postulate or theorem.

39. Exercise #5  State if the two triangles are congruent? If they are, justify your answer with a congruence postulate or theorem.

40. Exercise #6  State if the two triangles are congruent? If they are, justify your answer with a congruence postulate or theorem.

41. Exercise #7  State if the two triangles are congruent? If they are, justify your answer with a congruence postulate or theorem.

42. Exercise #8  State if the two triangles are congruent? If they are, justify your answer with a congruence postulate or theorem.

43. Exercise #9  State if the two triangles are congruent? If they are, justify your answer with a congruence postulate or theorem.

44. Exercise #10  State if the two triangles are congruent? If they are, justify your answer with a congruence postulate or theorem.

45. Closure Take a moment to response to the following prompts on a flashcard or in your notes.  What is required in order for the base angles of a triangle to be congruent?  In order for the base angles of a triangle to be congruent, the ___________________________.  What is required in order for two right triangles to be congruent?  In order for two right triangles to be congruent, the _____________________.