Download Geometry Fall 2011 Lesson 17 (S.A.S. Postulate)

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Lesson Plan #25
Date: Monday October 31st, 2011
Class: Geometry
Topic: Base angles of an isosceles triangle
Aim: What is the relationship between the base angles of an isosceles triangle?
HW #25:
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
Do Now:
1) Using a straight and compass and straight edge construct the angle bisector from
vertex B intersecting ̅̅̅̅
𝐴𝐶 at D.
2) How many angle bisectors can you draw from B?
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
̅̅̅̅
Given: ΔABC with ̅̅̅̅
𝐵𝐴 ≅ 𝐵𝐶
Prove: < 𝐴 ≅< 𝐶
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Statements
Let ̅̅̅̅
𝐵𝐷 be the bisector of vertex < 𝐴𝐵𝐶,
𝐷 being the point at which the bisector
intersects ̅̅̅̅
𝐴𝐶 .
< 𝐴𝐵𝐷 ≅< 𝐶𝐵𝐷
̅̅̅̅
̅̅̅̅
𝐵𝐴 ≅ 𝐵𝐶
̅̅̅̅
̅̅̅̅
𝐵𝐷 ≅ 𝐵𝐷
Δ𝐴𝐵𝐷 ≅ ΔCBD
< 𝐴 ≅< 𝐶
C
A
Reasons
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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 𝐴𝐷
𝐶𝐷 , we deduce that the
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
Assignment #1: Complete the proofs below
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Assignment #2:
10.