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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 weeks lesson on triangle congruence analysis. We will review the pre-assessment. You will have 15 minutes to complete the post assessment. September 20, 2013 1) Sit. 2) Materials out. 3) Backpacks away. 4) Do Now SILENTLY.

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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)

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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.

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Angles of Isosceles Triangles Pg. 236 in Geometry textbook

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Investigate Isosceles Triangles Pg. 236 in Geometry textbook

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Base Angles Theorem Pg. 236 in Geometry textbook

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Base Angles Theorem Pg. 236 in Geometry textbook

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

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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:

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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:

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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:

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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.

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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.

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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.

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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.

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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.

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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

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Hypotenuse-Leg Congruence Theorem

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

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

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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?

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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?

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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 _____________________.