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Transcript

1 Lesson Plan #024 Date: Friday November 13th, 2015 Class: Geometry Topic: Base angles of an isosceles triangle Aim: What is the relationship between the base angles of an isosceles triangle? HW #024: B Note: Postulate – A whole is greater than any of its parts. Objectives: 1) Students will be able to use the theorem that states that the base angles of a triangle are congruent Do Now: 1) Using a compass and straight edge to construct the angle bisector from vertex B intersecting at D. 2) How many angle bisectors can you draw from B? A Postulate: Every angle has _________________________ angle bisector PROCEDURE: Write the Aim and Do Now Get students working! Take attendance Give Back HW Collect HW Go over the Do Now 1. 2. 3. 4. Given: ABC with Prove: 5. 6. Statements be the bisector of vertex , being the point at which the bisector intersects . Let (s s) ( a. a.) ( s. s.) C Reasons 1. Every angle has one and only one angle bisector. 2. 3. 4. 5. 2 What theorem have we just proven about the base angles of an isosceles triangle? Theorem: If two sides of a triangle are congruent, the angles opposite those sides are congruent or the base angles of an isosceles triangle are congruent. What other parts are congruent? Definition: A corollary is a theorem that can easily be deduced from another theorem. Since bisector of the vertex angle of an isosceles triangle bisects the base. Corollary: The bisector of the vertex angle of an isosceles triangle bisects the base. Corollary: The bisector of the vertex angle of an isosceles triangle is perpendicular to the base. Corollary: Every equilateral triangle is equiangular Note: Differentiate between the definition of a midpoint and the Midpoint Theorem. Definition of a midpoint – A point on a line segment that divides the segment into two congruent segments. Midpoint Theorem - A midpoint divides a line segment into two segments, each ½ the length of the original segment. Similarly distinguish between the definition of an angle bisector and the Angle Bisector Theorem. Assignment #1: Complete the proofs below , we deduce that the 3 Assignment #2: 10. 4 If enough time: 1) 2) 3) 4) 5) 6)