Download Geometry Fall 2015 Lesson 024 _Base Angles of an Isosceles

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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)