Parallel Lines and the Triangle Angle-Sum Theorem

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Presentation transcript:

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: Example: A triangle with two congruent sides. Example:

Scalene Triangles Definition: Example: 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: Example: A triangle whose angles are all acute. Example:

Right Triangles Definition: A triangle with one right angle. Example:

Obtuse Triangles Definition: Example: 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.