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Parallel Lines and the Triangle Angle-Sum Theorem
Geometry
Mrs. King
Unit 3, Lesson 3
Theorem 2-1Triangle Angle-Sum Theorem
The sum of the measures of the angles of a triangle is 180.
Video: Sum of the Angles of a Triangle
Find the measure of the missing angle
http://www.mathsisfun.com/geometry/images/triangle-missing-angle.gifhttp://maths.fallibroome.cheshire.sch.uk/triangle.jpg
http://www.gizapyramid.com/basic_triangle_w-angles.gif
x
x
Practice
• Find all Variables:
Practice
• Find all Variables:
Practice
• Find all variables
Definition
Exterior Angle: an angle formed by the side of a polygon and an extension of a side.
http://www.freemathhelp.com/images/lessons/exterior1.gif
Definition
Remote Interior Angle: the two nonadjacent interior angles to an exterior angle.
http://www.freemathhelp.com/images/lessons/exterior1.gif
Theorem 2-2Exterior Angle Theorem
The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.
Find the measure of the missing angle
http://www.kwiznet.com/px/homes/i/grade8/math/Grade_VIII_Triangles_And_Polygons_PB2_QuestionNo.5.gif
Find the measure of the missing angle
http://www.freemathhelp.com/images/lessons/exterior2.gif
Definition
Corollary: a statement that follows directly from a theorem.
Corollary to Theorem 2-2
The measure of an exterior angle of a triangle is greater than the measure of either of its remote interior angles.
Types of Triangles (by sides)
• Equilateral
• Isosceles
• Scalene
Equilateral Triangles
• Definition:– A triangle with three
congruent sides.
• Example:
Isosceles Triangles
• Definition:– A triangle with two
congruent sides.
• Example:
Scalene Triangles
• Definition:– A triangle with no
congruent sides.
• Example:
Types of Triangles (by angle)
• Equiangular
• Acute
• Right
• Obtuse
Equiangular Triangles
• Definition:– A triangle with three
congruent angles.
• Example:
Acute Triangles
• Definition:– A triangle whose
angles are all acute.
• Example:
Right Triangles
• Definition:– A triangle with one
right angle.
• Example:
Obtuse Triangles
• Definition:– A triangle with one
obtuse angle.
• Example:
The three sides of the triangle have three different lengths, so the triangle is scalene.One angle has a measure greater than 90, so the triangle is obtuse.
The triangle is an obtuse scalene triangle.
Classify the triangle by its sides and its angles.
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