Learning Goal:  IWBAT to solve for unknown angles in triangles by using the triangle congruence theorems and 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. September 20, ) Sit. 2) Materials out. 3) Backpacks away. 4) Do Now SILENTLY.

Agenda: 1.Do Now (15 min) 2.Base Angles Theorem (30 min) 3.Hypotenuse-Leg Congruence Theorem (35 min) 4.Midsegment Theorem (35 min) 5.Closure (5 min)

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.

Angles of Isosceles Triangles  Pg. 236 in Geometry textbook

Investigate Isosceles Triangles  Pg. 236 in Geometry textbook

Base Angles Theorem  Pg. 236 in Geometry textbook

Base Angles Theorem  Pg. 236 in Geometry textbook

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

Base Angles Theorem Practice  Using the Base Angles Theorem and its corollaries, find the value of x in the exercises below. Problem:Theorem:Why Important?As a result:

Base Angles Theorem Practice  Using the Base Angles Theorem and its corollaries, find the value of x in the exercises below. Problem:Theorem:Why Important?As a result:

Base Angles Theorem Practice  Using the Base Angles Theorem and its corollaries, find the value of x in the exercises below. Problem:Theorem:Why Important?As a result:

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.

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.

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.

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.

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.

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

Hypotenuse-Leg Congruence Theorem

Are the following pairs of triangles congruent? If they are, justify your response with a congruence theorem.

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

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?

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?

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 _____________________.