September 20 , 2013 1) Sit. 2) Materials out. 3) Backpacks away. 4) Do Now SILENTLY.

1. September 20, 20131) Sit. 2) Materials out. 3) Backpacks away. 4) Do Now SILENTLY. Learning Goal: • IWBAT to solve for unknown angles in triangles by using the triangle congruence theoremsand the base angles theorem. Homework: • HW 3.7: Isosceles and Equilateral Triangles Worksheet ------------------------------------------------------------------- Do Now: • Take out a pencil and prepare for the post assessment for this week’s lesson on triangle congruence analysis. • We will review the pre-assessment. • You will have 15 minutes to complete the post assessment.

2. Agenda: • Do Now (15 min) • Base Angles Theorem (30 min) • Hypotenuse-Leg Congruence Theorem (35 min) • Midsegment Theorem (35 min) • Closure (5 min)

3. Retake Quizzes: • 10th and 11th 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. Angles of Isosceles Triangles • Pg. 236 in Geometry textbook

5. Investigate Isosceles Triangles • Pg. 236 in Geometry textbook

6. Base Angles Theorem • Pg. 236 in Geometry textbook

7. Base Angles Theorem • Pg. 236 in Geometry textbook

8. Corollaries to Base Angles Theorem • Pg. 236 in Geometry textbook • The Base Angles Theorem leads to the following corollary.

9. Base Angles Theorem Practice • Using the Base Angles Theorem and its corollaries, find the value of xin the exercises below.

10. Base Angles Theorem Practice • Using the Base Angles Theorem and its corollaries, find the value of xin the exercises below.

11. Base Angles Theorem Practice • Using the Base Angles Theorem and its corollaries, find the value of xin the exercises below.

12. 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.

13. 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.

14. 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.

15. 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.

16. 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.

17. 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

18. Hypotenuse-Leg Congruence Theorem

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

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

21. 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?

22. 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 side parallel to the midsegment?

23. 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 _____________________ .