Download Geometry Fall 2016 Lesson 025 _Base Angles of an Isosceles

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Lesson Plan #025
Class: Geometry
Date: Monday November 14th, 2016
Topic: Base angles of an isosceles triangle
Aim: What is the relationship between the base angles of an isosceles triangle?
HW #025:
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) How would you classify the triangle at the right? Why?
2) What relationship exists between the sides opposite the congruent sides?
3) Based on the observations from above, we can conclude that if two sides
of a triangle are congruent, then the angles opposite those sides are
congruent. Do our observations and conclusion demonstrate deductive
reasoning or inductive reasoning? Why?
PROCEDURE:
Write the Aim and Do Now
Get students working!
Take attendance
Give Back HW
Collect HW
Go over the Do Now
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Assignment #1:
1) Using a compass and straight edge to construct the angle bisector from
vertex B intersecting
at D.
B
2) How many angle bisectors can you draw from B?
Postulate: Every angle has one and only one angle bisector
Given: ABC with
Prove:
1.
2.
Statements
be the bisector of vertex
, being the point at which the
bisector intersects
.
Let
(s  s)
3.
4.
( a.  a.)
( s.  s.)
5.
6.
Reasons
1. Every angle has one and only one angle
bisector.
C
A
2.
3.
4.
5.
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:
, we deduce that the
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Assignment #2: (Engagement) Complete the proofs below in your groups.
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Assignment #3:
10.
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If enough time:
1)
2)
3)
4)
5)
6)