Download Geometry Fall 2015 Lesson 027 _Inequalities involving sides and

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Lesson Plan #27
Class: Geometry
Date: Wednesday November 18th, 2015
Topic: Inequalities involving sides and angles in a triangle
Aim: Inequalities in involving sides and angles in a triangle.
HW #27: Page 222 #’s 1, 2, 4, 5, 7, 8
Do Now: In pentagon ABCDE, draw in an exterior angle at vertex E
Find the measure of an exterior angle at vertex E of polygon ABCDE.
Definition: An exterior angle of a polygon is an angle that forms a linear pair with one the interior angles of the polygon.
For each exterior angle, the interior angle that it
forms a linear pair with is called an adjacent interior
angle. The remaining two angles are called the
remote interior angles.
Theorems presented without proof
Theorem: An exterior angle of a triangle is greater than the any of the two remote interior angles or An exterior angle of a triangle
is always larger than either opposite interior angle.
http://www.mathopenref.com/triangleextangletheorem.html
This proof provided at end of the lesson
Theorem: If the lengths of two sides of a triangle are unequal, the measures of the angles opposite those sides are unequal and the
greater angle lies opposite the greater side.
Theorem: If the measures of two angles of a triangle are unequal, the lengths of the sides opposite these angles are unequal and
the greater side lies opposite the greater angle.
Online Activity: http://www.mathopenref.com/trianglesideangle.html
Assignment #1: Complete the exercises below.
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Regents Exam Questions:
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Appendix 1