Parallel Lines and the Triangle
Angle-Sum Theorem
Geometry
Mrs. King
Unit 3, Lesson 3
Theorem 2-1
Triangle 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://maths.fallibroome.cheshire.sch.uk/triangle.jpg
http://www.mathsisfun.com/geometry/images/triangle-missing-angle.gif
x
x
http://www.gizapyramid.com/basic_triangle_w-angles.gif
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 2-2
Exterior 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:
Classify the triangle by its sides and its angles.
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.