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Instructor: Qian Bradley Subject: Properties of Isosceles Triangle (Geometry) Content Goal: 1. Review the definition and vocabularies of the isosceles triangle: a. an isosceles triangle is a triangle with at least two congruent sides b. a triangle with at least two congruent sides is an isosceles triangle 2. Isosceles triangle conjecture: if a triangle is an isosceles triangle, then the base angles are congruent 3. Converse of the isosceles triangle conjecture: if a triangle has 2 congruent angles, then it is an isosceles triangle. 4. Apply algebra to angle properties Literacy Focus: Math vocabulary and responsive teaching in a ThreePart Learning Framework a. Pre-learning, review vocabularies with the students: i. isosceles triangle ii. vertex angle iii. base iv. base angle v. leg vi. equilateral triangle vii. congruent viii. conjecture ix. converse b. During-learning, assess students vocabularies through in-class activities c. After-learning, use the triangle-square-circle method, let the students write in their notes AZ State Standards: 1. MHS-S4C1-06 Solve problems using angle and side length relationships and attributes of polygons. 2. MHS-S4C1-10 Solve problems using right triangles, including special triangles. 3. MHS-S5C2-02. Solve problems by formulating one or more strategies, applying the strategies, verifying the solution(s), and communicating the reasoning used to obtain the solution(s). Prerequisites: 1. Understanding of the isosceles triangle definition (Chapter 1) 2. Understanding of Algebra Instructional Objectives: Objectives 1. Review/reflect the definition of the isosceles triangle and the related vocabularies. 2. Solve problems related to the conjecture of the isosceles triangle and its converse. 3. Apply algebra to angle properties Assessment In class discussion In class activity: worksheet In class discussion In class activity: worksheet Instructional Procedure: Warm up: Review the definition and vocabularies of isosceles triangle Questions to ask: Rhetorical: Anyone remember what is an isosceles triangle? Review/reflect from Chapter 1 that an isosceles triangle is a triangle with at least two congruent sides. In an isosceles triangle, the angle between the two congruent sides is called the vertex angle, and the other two angles are called the base angles. The side between the two base angles is called the base of the isosceles triangle. The other two sides are called the legs. Question to ask: Rhetorical: Is equilateral triangle an isosceles triangle? Anticipatory hook: Euclid (Greek mathematician from 300 BC.), is popularly considered as the "Father of Geometry". He is believed to have been active in Alexandria, during the reign of Ptolemy I (323 BC–283 BC). Euclid’s Element Book I Proposition 5 stated a conjecture - In an isosceles triangle the angles at the base are equal. Pappus (Greek) who followed him gave a clever proof of this theorem. Transition: distribute the worksheet Ask the students to make sure look at the worksheet page 1. Question to ask: Managerial: Everyone with me on page 1 of the worksheet? Lecture: The isosceles triangle conjecture: If a triangle is isosceles, then base angle are congruent. Example: Find the missing angle “x” Class Activity: Worksheet page 1 1. Ask the students to think about the 1st problem, get their initial thoughts. Then model the solution. 2. Ask the students to work on the 2nd problem. Ask for student volunteers. Lecture: Converse of the isosceles triangle conjecture: If a triangle has 2 congruent angles or 2 congruent sides, then it is an isosceles triangle. Example: Class Activity: Worksheet page 2 1. In class discussion. 2. Ask the students to think about the 2nd problem, get their initial thoughts. Then model the solution. Closure: Introduction to Triangle-Square-Circle method: what are the 3 most important things that you learned today, what squares (clicks) with your interest in math, what question still circles around your head? Students do their own reflective writing: call out 2 students to read what they write and share.