This document discusses triangles and triangle theorems. It reviews the different types of triangles such as acute, obtuse, right, equilateral, isosceles, and scalene triangles. It also covers the exterior angle theorem, which states that an exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. The theorem is then proven using properties of supplementary angles and the triangle sum theorem.

1. Ch4.1_TrianglesTheorems.notebook October 24, 2011
Chapter 4.1
Triangles and Theorems
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2. Ch4.1_TrianglesTheorems.notebook October 24, 2011
Review
All angles in a triangle add up to 1800
Acute triangles: all angles are less than 900
Obtuse triangles: 1 obtuse angle, 2 acute angles
Right triangles: 1 right angle, 2 acute angles
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3. Ch4.1_TrianglesTheorems.notebook October 24, 2011
Review
Equilateral triangles: all sides are same length
Isosceles triangles: Two sides are same length
Scalene triangles: all sides have different lengths
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4. Ch4.1_TrianglesTheorems.notebook October 24, 2011
600
200
600
300
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5. Ch4.1_TrianglesTheorems.notebook October 24, 2011
Exterior Angle Theorem
An exterior angle of a triangle is equal
to the sum of the 2 nonadjacent angles
in the triangle.
600
0
1200 60 600
Find x
x
300
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6. Ch4.1_TrianglesTheorems.notebook October 24, 2011
Proof of External
Angle Theorem
C0
X0 Ao Bo
0
X + A = 180 Supplementary angles
0
A + B + C = 180 Triangle sum theorem
X + A = A + B + C Transitive Property
X = B + C Addition property of
equality
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